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Stability of Minkowski Spacetime...
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Erkannte Entitäten
Sprachtranskript
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and we have to do so a festival of electoral thinkers the organizer fall as invitation to the kids and and so it today and we took you about the nature of wizard transactions in trade but 1st order we introduce you would attend as a context so the engine letting seizes space then there is described the value for money for independence equipped with a real intent between gene so usually many Florida is on or off all the management under solo Anthony triggered submit trigger with signature of minus 1 1 1 unsold as denigration the image as the geometry of the universe to the distribution of of matter and energy which is present on the they can be however you knew minus 1 the the new sold I will explain what it is and you knew to themselves against the desert sewing described to kill richer others the trade and there you can see it as as a model of the money Alboreto on Dimitri G. and roughly speaking to them promptly plans could be related to the abreast of review of DG Cambridge it is this kind of curvature it is trace of the reach themselves Air under a solid union you it is Dimitri K. the ruins and between and the new new inducing antiimpotence himself it is the object which described as the the distribution of matter energy on it's a fallen depends on the matter more than the city has a different phone as always to India graphics created all underestimating the him but in the in our case we will take the new new people in the room soldiers and veterans the reasonable matter and should takes a trace of integration you take are nose when I've looked off they went out days the trace of genuine new equals rule on so you that ask is equipped with 0 unsold and standard question veteran forces just that in looking for your insanitary G which are that was rich in terms of army is equipped to do so at the Vatican estimation is given by I mean customer trades because this is the end of this season for equipped to resubmit pain which is a member of the committee square close to the extent of the grand plans of the extreme right that's a so these entreaties flattening trade but it's not the the only solution to work and sharing the creation of an immaculate attorneys cents is broad and vague around to see a week in rightcenter any question as a cushion for so the that 4 Shannock which out triplex see demand you claims it is against the desert that half of what is a space so much the spacewalk like at some instant equals on what is its speed of propagation at sequence 0 student information 3 so Sigma is the freedom to face Sweeney referring to geographic easily mandatory Bloomberg a unitary to themselves a UN to silence any question with this initiative backed up consistent feigning injury to reassure the of giant Micron region with which orphanage equals 0 and surges that stigma embedded in the game the energy restricted to see demand is that the Romanian that fringe about on day his assumed from them and phone after the meeting of the minds that you can see again as the day that at attend secrecy the nearest their religion with respect to time offices in each region the condition that they can and each was an arbitrary because some of us there there is a question that event onions initialed at the allows the creation of new ones you move moments when part of the AlJazeera include Grand rule from around the world and quarters so they can be attorney as Graham's case square plans to spread because you will wear Alabama is a strange is Ricci so it into this caricature of although injured I think the trace of the registers of offered about and gays who it's said yes is taken with respect to the nitrogen back Ontario His traces of schools in the
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unsolicited this equation on the very question can be returned to the marriages of gay members brilliant all of his so the stagnation which our depend on the ones that are Fuji about gay and better ones are solid and denigration are looking westwards through this green button Surinamese unit we wanted to out times if he still under its saying that so for alienation that the demand geographically within the frame so this is not good the solution of the constraints no other localities strands of solutions to the state which but usually have the solution cannot be at the remaining sir we never see it again I think singularity may follow the events issue will continue ventilation of party cannot rule restoration and then you may have hope that there is a growing existence on so this is a game a followup the is based stem from must students and so as a nation that of our funding goes to space then urges candy for onstreet agreed reserve hidden between that on the symmetry to turn which is 0 but it could be a fool but the thing you can also imagine because the Minkowski space time that they draw here on broad and an identification and he's on the new we obtain and those evaluation that as it but let's consider this under issue page so service of was sole provide system In men's season there that it should take an Indonesian that assets costfree and G about pleaded with their sewage Djiboutian data having of regularity after his close to and within down played the smaller and some stands on those who you assume that there's that that it is sum that include flats this means edgy about stands for their staff that Infiniti with sold at a rate of Gatien principles here wrote at the impunity then you have no matter the sense of solution of the convergence of eradicating the 3rd to make prosecuting so there is another proof of this theorem which is due to work I mean that the Indians cable which was is and waved gardening and the winner extenuating weight coordinates so in the stock had renewed so interesting is its any fear of Mingus Dynasty unit takes different as is the case or in the presence of the translation symmetry so
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so we wasted many foreign debt Of the phone off falls the decomposing and
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often on its streets and Pequea that with intrigue of the phone g Falwell's Free Press when the trade accord the menace to find G because fight the extreme square where gene is a cemetery on plan on this 1 all of us to what time of the ongoing users cannot function when we assume that he owns a raft of independent of the coordinator extreme Serena and energy the alliance press and then mentioned but immigration flow and you assume that the energy fall set aside expenditure aggression we obtained as well as you stand up for what he Orange which is that the number China in symmetric G but he is equal to 0 on Zaritsky themselves of G In court convenience the now so this is no system of immigration in after press work so there is a Vatican absolution for gasoline inventories which is actually Minkowski spacetime and units onedimensional offense because question is space than either of symmetry in battleground as the translation symmetry on this solution and some interesting solution the rest homes was a solution he quietly rule under pool zone because the new into press when mentioned of the course and commands the screen because the extends Crown until then turned into a question I went in asked Is there is a solution and stable for the system it's just me made it needed was more amount that's as he served as the answer to this
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question is not the event by the sustainability of Minkowski spacetime makers who played on and on about Lewinsky because of estimation we consider other transition symmetry so emphatic enough talent as some to take effect in Sri present dimension because of the new cannot perform better at ingenuity to work Tuesday could then be tricky issue after remains the same as in 1 direction and so we know the US as himself to the salinity the amendments the 1st pillar communal precisely I need to interview wept as the initial we didn't we would think so the initial letter should be a solution of the "quotation mark declaration so there's uh and then I works and China constraint equation in natural but if you want if you are not in the commission of an energyefficient himself as it would be the case here we have a right inside integration it just means that 2 of right and signed them up on the constraints so here this western side is given buys it at that at Antigua 0 of the undertaking so this would be given to need issue identity cards you on then we can look for solution of the constraint equation of the form G mass to win prosecution and on through to the bus carrying on without loss of generates the Cincinnati Bell now is the time it reached on Oct tool we can assume that you back is a user control my class of the condemnatory of Jabalya across he too long that standard not only can also be composed came into ways that trace a spot on the it's Tracy independently we writes cake Gordon H. press 1 out of GE Temporao style is a trace of this means furniture and so frankly and so it is a constraint question the concedes no inundated the existing flow harder longer on H on that route aged please dollars seen as a barometer of so it's OK because they're so wooden and that's what we're think 1 function on the 20 slaves it themselves In a symmetric faced on solving twodimensional itself to work as to twocomponent with component on the S3 3 constraint equation in an imprisonment Chancellor we
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have the right number of creation of the retinal often the ones that surrender the use of fully in so Castro that she'd beaten she has there been an H 2 days Edgware and thus implicitly assumes that their combined people teach some will be on longer assume that there signs we have seen under we also take but some solution analysts and there are you know each 1 a convection surpassed even we out ones we see them in the attorneys of freedom over on then there exists so there is a set of parameters of the 0 8 1 2 in parameter is 0 A 1 2 was the WTO and the 2 you will need aid the entire under there exists Munich solutions known that H commissioner constrained it means not that he told 2 men used a 0 0 tie in with the function which is at Infinity on 0 up in the middle Diane Kruger resemble half dressed it's also take the data thousand Bloomberg between you and press that the move of wondered for is that a Each applicant also right from the repayment plan program for ThinkEquity trees mattresses and complicating and now is not so what is the is not quite free so is equal to where the miners from that diner and he will run out of time there weren't whose use of Saddam a the news I have seen the press you may notice from there but need playing time so it is better In the past with on the small sedan was aware of coordinated center the In the 1 and there it didn't mean summer's most commands so here and see that there is no is not so it's not so much of Rivera does unity freedom is their choice of dysfunction and without the use of is imposed 2 others the right set of tools 190 condition to invest they need to exist and formed their own age also L the Bernie at a 0 the end of on which is a source of them in the development of from that is all of us this means as a military chair Dimitri G. back here is that under the as an intriguing accord With additions have done their duty value given by a 0 a under debris metallurgy and you you'll see deputy that he is is the development of incessant into development of H and Eucharist monsters here on rearmament so so I just want to give you a precise needs to ensure that our weakens but on the amount of invades the nervous dominating urine so no pictures of the meeting the will assume a more regularity than it damage wonderful isn't very consistent with intentions to inches 29 very Ed conceded now did you read is not a simplification it's really we need it there to assume that their convictions evoking amusing to offer and then take to tower to vary from members you want to see a private timber and then Zaidi Shiite upholds of the following the remnants early needs to work a little less solution so there exists the resolution g could see the development of the nation that even by his previous Surin said said that's so too is ready we actually can introduce to coordinate system with 2 coordinate system the 1st quality next Tuesday and the things that I see the future of of the view of the future of the initial that of all the so in this area insists said we have a lot in a sustained the critics want to exclude suggests we Jenna I was a make she is then a constant diet here directions 1 of the most famous client by 1 few where most onetime under gene minus 13 customer treating to press 1 is less than it's Sheena and find 1 person on most of the time where his refusal to extend invitations after the top of the for and his partners team continue please tell me this under In videos in a in the complement of some compliments we have a Anderson according sustained the prime it's like from which to Prime so there is no need invest in the complement of seemed to give you this team itself unique was that she is equal to 0 by the French and we have in the future offer descent when she is none the worse for is the complement of insects so they actually get into so we just need to know
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a gene on the looked convincing wizarding customer treatment with Amazon between GM on Read's edgy miners GA is less than the between stance than its you time 1 because as on most 1 5 times 1 1st Q 1 president ,comma it was then that is a permitted between 1 5 to 1 on the is imperative that we have to putting through the surrender of 2 events in each other a UN so how would they what to this mentoring GAO which is not true because GM so a series you should put here as prime London should trying because it is itself the will you take care our privacy to me is the product of the debt associated to the deprived coordinates on this primed to prime defined by the friend 1st to prime apartments to prime sold GAF to express its in in coordinates with Premier this is the difference Grant the young prince Scranton note the damage GTE Diamond a deep troop price this is the price yes are primed to rescue Prime Time ABC will test 81 course seemed primed with 8 to 10 feet of crime square isn't that correct so the sponsored the GDP 8 0 8 1 8 2 the was a quantity which have given by as this year and for the nation at this point prescribed as intended and on this metric is not Dimitri because it doesn't attended at infinity this means that if you will working with emphasis support his assumptions used in the forest was supported by the middle work so FordhamInstitute your lower because of personal read books official government fearful of that supported the systematic use of remote old job perturbation somebody supported is this but you know there's a symmetric Federation is given by the year of which using genetic that was the only freedom when philosophy even the only freedom in some small way done uh in the choices of those encourages this is not free of freedom justice and that's what I explained in a year that faulty because key event from because geometric who stands at more than the freedom To ensure that if you want some of that sequence all would be disability if you want the supporters so I cannot here the stability of cost it's not same Europe if you have always supported research so how hard this view of the I want to do is to play a it's the thing is that award Federation but if you wanted us about emission Owings press 1 that uh it's not so it's not in the setting of fetal canine because with those of the translation symmetry left to enter so the owners of the a direction in which the U.S. symmetric and symmetry you are not assented to the fat so you are not so it's another fitting it's not in the city you you can assume that she's going back to both the dead undefined afterward but inside is not combat is supposed to Fuego back to Sweden agenda we had a few extra using express direction before then because symmetrically and that's I like you know additional weaponry at in mishandling his kidney members of the the jury awarded the 1st to be history of then I don't exacerbate the condition continues at the end of hold so I don't know like interpretation will answer to this so it so no evidence here as in the remaining years of the token the EU summit its approach that will make you understand why why any of to coordinate assistance tool to describe my solution because it seems and the strange adjoining can also introduce will buy the standard fuel Texas grew by quality stance a you renascent instead of GE which is quite nice to us we have some of unitary instances b so maintenance so this strategy for provisions surrendered buyout from proof of 72 of by that run women's so we will introduce wave coordinates with before of using them that's just right readers of which themselves in some of the incident can I don't assume anything underscored its ascent on then Uganda's computer you know that's the Richardson said in writing that they would achieve of the Christopher warranted of were not like the original symmetry to just varied compare that competition and even that Armenia was like 1 minus 1 out of the downed Shannon in the military G of the military component you go some quadratic down communities that some dance which over the phone GE and a full menu the new each hole and you take scenic recuse wideranging New year would New which will wear H it's something which depends on quantity would depend on the derivative of gene which can be lifted like 1 of those is cruel to the dominant Of the military G. the transfer of GE and filed with the
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work of the determinants when the industry out of adjustment that protects the interests of the matrix and this is just looking but domination in the metering G of the coordinates function thanks "quotation mark cancelation date it should assume that your quality its functions that assets at age 40 when the you up in the socalled right coordinates was then alSistani Mayor of Christian which was an there was the scarf in white coordinates it can be returned likeness then offered a lesson in now weighty questions to Clinton that I mentioned their machetes Entergy of key questions you will understand actions in region of Jimi you is that I minus to the new clean and fuel players some quite rightly damage analogy this equation always do we have an existence of the best solution for this then 12 or more it's more than under tool 11 he had just to give you would have been far the away the equation in this so as antigay offered the immunity of she satisfies the weighty question in indigo sky we as a nation that asking the new uh negating it's a Quebec is superseded that on the outside it's none when an assumption we have fulfilled then but their events he or she has the following day the Gaelic select because it shows that there are also used to run over 1 this is 1 time 1 person we have and should take some of not rundown there each year but what upwards with their achievement you have modernday the so that when the events laughs inventory was respected as well as his office you can also take part in the streets a few of them have contingent with the meaning of the Lands End you have not the gate of the year actually like kids Glenn Spencer we on the 1 person to wonder so this implies that the issue you know 1 thing they have been on the where the creation Of the no only share on you would you continue funding because it said it is late with its interview with more than 12 hour fall program as an issue assume someone's front 1 you wish you that you satisfies the same as meant as a would set it as the a solution to the free wave equation would set aside until was charged another teammates when he she wants recovery to work and in enters the missile unit supplied by the Q 1 you integrated I knew then that the emergency as integral the you square video lessons in words of player and then you do under deal with the matter 1 official data making it shooting reasons this is make this is based on that consideration Over a and almost all of the as the decline of the you square that is the position and fuel uh which we assume to be bonding because it's part of the United that the managers of the on so you would think that this is less than that seemed to see President right from jeans plaid on so the manager of the EU's planned is growing and like it sooner insisted on time "quotation mark of it all and so on and please and so if you want to what struck and you learn to recall them anathema to Madonna you need to assumes that the incident 10 "quotation mark of tea is bonding consul you have existence and the the rise less than 1 overnight incident square the group producer wheat wheat yes we assumed we assume that that's you that satisfies the Senate's connected with such sites which are not their best and requires you this is that the conclusion of substances for a division of the use of funds arms no it's as a conclusion In London the this is the message that you on the way hadn't some in In the 1st of all you want to include provisions to the review when was the last day of the year grumbling in the U.S. will assume his unilaterally this is the right 1 you have to be on the inside of the from way the and then you integrate the solution to the problem here In
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the light of the only 1 and what of the morning session that we have to let it sit underwent a graduate we obtain square root of team and if we wanted to get back to work this Monday that we obtain that we have to to assume that the students and 1 of students and but history of some structural problems and I mean everything that comment and was like new entangled with the American work force at the end of the year and then when we do the same thing if we find them but if we have integrated the value we ate we use of this image we have filled with derivative of fuel I then what we obtain is that the we have instead of it's the time 1 of the root of the we decreases we unsolicited into rebel and there is a demand exists N I'm so so his his unit was due to push again for this particular case but area there were some resort to buy and manage policy enough of them so unfortunately and Johnny questioning wife coordinates don't Underwood structure to structure we need to introduce new friend to any predictions because they are paid by employer the claimant is the on you before the entailed on the interests of Kansas frame the shiny creation can be return so if we drop was a any marriage that's involved that the within the video because then we have of decay to work out a little better results than what remains is the nomination but he declared to the world that under channel so menus G and then did you she squared off in court Tuesday ruled the nomination of G and said menus you only need to square the cleared in particular 0 unbounded Sharon Perugini invented by menus jeered and due to stringent about about people and so the uneconomic kept as a quirk was enough which you want to but they way they offer of but but in front of them there is a temperatures GSA on the thing and the right inside and on capsule a DQ Hispanic was assumed that chair doesn't have the narrative on then so this seems to be that but the weekend as the weather and sure enough forces unity of me go skiing like Gordon with this when the free use of the wave coordinator condition we obtain and that's the city of your relation between some derivative of J and the batted throughout interviews at the derivative of G8 and Ben derivative of GM and is like derivative of samples questions of matrix and so the down which survivors the and you are right to family of the structure so we can regulate them on we are left with the 4 races than there are mentioned words you never mentioned generalize about quantitative so we try to speed up political conventions as he said and this structure over the worst year the structure was going to it's trade and there was introduced also by the wins on the entitles them to approval by the existence of that we some the gamut sneak lost due to the fact that here there is no the L so in Striptease went In Bloomberg existence and that we stand summary evidence scrubs Clemens standard is only like a number of communities 19 Alcazar as a loss is more dramatic because of what they said you have the worst in the Anahuac square with the so actually there this evening just because we did not choose that's why we did not choose the right coordinates under this group recalled to receiving these began as soon as we can assume that we have formed a new idea on coordinate since then it is ideal community stands every matriculation as in the game we win the would we want that is in the details of a solution to the weighty question which is 1 of the square root of and in instead ideology L yet it is so we estimate that in its annual then we can ride sometimes and there's an it's the from the and then in despite your regarding stand with computers to reach themselves are bad the 1 underground rock which is only to the Jews ground which is equal to grant we can compute that it is 9 need to square the fondue you press so most down which are alleged to have seen on overstatement of the story he was have on this news alike on the season it's hidden when will that be on so what it means that the dam which would be the best 1 to deal with the this back down the question is not so energy and back as there would be there have been no way coordinates but it is G U I'm so much we can do is to impose a throughout the day and that is standard that would take care of this 1 it is
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by using without good dinner as well coordinated which of course instead of choosing age 40 quite was there all week this institute is equipped with a full and as a function as long as it does not depend on the directive of G we don't was like that would expenditure on what we can do is just to choose to us if we compute maturity and as fast H from which is an expression Intel was a derivative of the man contribution and convince them is that DQ what do you want to we just impose he imposes that Arafat HIV from using light air saying something right of the accused was granted as part of the cure for the Oval Office so imposing and then if we impose it this choice what we'll 10 instead of food the 3rd since then this is the family's the on what remains is a true beach moneyenough down without the structure which is originally and by please understand any laugh the future wonderful set should know With such a structure which is already the equivalent of free press went gaze on we obtain and Justin Leonard's maintenance the new compared to what meant just to the very quick work to conclude that this choice has some consequence season and it's amazing that means there is outside of the 18th ventilation and outsiders alike on Earth which is at the hearing and provided for the formation of the coordinates the inside their title Lakeland which is why we need to have some introduced to this thing called than if we want to have a nice description of all solution so thank think you were image of so that the people of the world "quotation mark canceled and legislators that the Conference USA mentions Levinson's acknowledgment of his life you gain just 1 onehalf of 1 of although it can be the same slowing things that you'd be going in and that the United States just lonely odyssey of structure yet so what told you that any understanding could you know that the said this surely down without no structure it appears on the floor about which is about the future injured about 1 units would
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be related the Aegean island of Bora Garrett make it's like syndicate of 120 forgery by that nobody would have "quotation mark of but this year we will still have the only in the interests of all just because this was the site of the world according to the you know it's a winner it's good enough because you again 1 of 2 people you want to have a say in the book which has sold more than you would use whatever you want to use the was the new law so that the but with the addition of a videotape of the scene this is equivalent to man into the region will not because it is a cruel management of Muslim and that which India's Kenneth King he is reside here during moment almost all of them used to conduct a supporter of the house so this is the importance of enjoying to here from the organizer of an and so without needing this assassination of very few cities all over the traditional to the old what is this the question because it is clear to those long period curious to hear what you would expect to see the result resulted in his fiction who was initially believed to have told the visiting room used to listen but during the same reasons without compatible to the assumption that only those closest to the investment through that year he put figure so I presume there no that you did the policies that on I don't think think all no it doesn't make any difference because then you have the Saskatchewan just have to some Molinari equation but says the watch will and still have a it's 1990 you you either in the structure so it doesn't it is transparent to in thank you do
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Distributionstheorie
Einfügungsdämpfung
Gewichtete Summe
Momentenproblem
Extrempunkt
tTest
Wärmeübergang
Gleichungssystem
RaumZeit
Gerichteter Graph
Richtung
MonsterGruppe
Deskriptive Statistik
Prognoseverfahren
Vorzeichen <Mathematik>
Gruppe <Mathematik>
Translation <Mathematik>
Wellengleichung
Vorlesung/Konferenz
Analytische Fortsetzung
Auswahlaxiom
Nominalskaliertes Merkmal
Addition
Oval
GrothendieckTopologie
Krümmung
Ruhmasse
Störungstheorie
Biprodukt
Ereignishorizont
Forcing
Verbandstheorie
Menge
Rechter Winkel
Beweistheorie
Konditionszahl
Ordnung <Mathematik>
Subtraktion
Folge <Mathematik>
Stabilitätstheorie <Logik>
Klasse <Mathematik>
Abgeschlossene Menge
Bilinearform
Auflösung <Mathematik>
Äquivalenzklasse
SigmaAlgebra
Symmetrische Matrix
Algebraische Struktur
Spieltheorie
Reelle Zahl
Massestrom
Äquivalenz
Oktaeder
Erweiterung
Determinante
GreenFunktion
Stochastische Abhängigkeit
Schlussregel
Unendlichkeit
Resultante
Matrizenrechnung
Prozess <Physik>
Punkt
Natürliche Zahl
Ausbreitungsfunktion
Familie <Mathematik>
Gruppenkeim
Kartesische Koordinaten
Inzidenzalgebra
Massestrom
Eins
Arithmetischer Ausdruck
Staupunkt
Einheit <Mathematik>
Regulärer Graph
Theorem
Existenzsatz
Unitäre Gruppe
Nichtunterscheidbarkeit
Gradientenverfahren
Wurzel <Mathematik>
Figurierte Zahl
Analogieschluss
Lineares Funktional
Parametersystem
Reihe
Stellenring
Frequenz
Zeitzone
Gesetz <Physik>
Arithmetisches Mittel
Betrag <Mathematik>
Tourenplanung
Strategisches Spiel
Geometrie
Koordinaten
Standardabweichung
Aggregatzustand
Nebenbedingung
Gewicht <Mathematik>
Ortsoperator
Sterbeziffer
Stab
HausdorffDimension
Gruppenoperation
Besprechung/Interview
Zahlenbereich
Derivation <Algebra>
Kombinatorische Gruppentheorie
Term
Division
Topologie
Symmetrie
Stichprobenumfang
Freie Gruppe
Zusammenhängender Graph
Optimierung
Grundraum
MinkowskiMetrik
Widerspruchsfreiheit
Schätzwert
Wald <Graphentheorie>
Kontinuumshypothese
Relativitätstheorie
Physikalisches System
Primideal
Integral
Objekt <Kategorie>
Energiedichte
Singularität <Mathematik>
Quadratischer Raum
Quadratzahl
Flächeninhalt
Mereologie
Numerisches Modell
Metadaten
Formale Metadaten
Titel  Stability of Minkowski Spacetime... 
Serientitel  Trimestre Ondes Non linéaires  June Conference 
Teil  05 
Anzahl der Teile  23 
Autor 
Huneau, Cécile

Lizenz 
CCNamensnennung 3.0 Unported: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. 
DOI  10.5446/20813 
Herausgeber  Institut des Hautes Études Scientifiques (IHÉS) 
Erscheinungsjahr  2016 
Sprache  Englisch 
Inhaltliche Metadaten
Fachgebiet  Mathematik 
Abstract  Stability of Minkowski Spacetime with a translation spacelike Killing vector field In the presence of a translation symmetry, the 3+1 vacuum Einstein equations reduce to the 2+1 Einstein equations with a scalar fi eld. We work in generalised wave coordinates. In this gauge Einstein equations can be written as a system of quasilinear quadratic wave equations. The main diffi culty in proving global existence of solutions for small data is due to the weaker decay of free solutions to the wave equation in 2+1 dimensions, compared to 3+1 dimensions. This weak decay seems to be a deterrent for proving a stability result in the usual wave coordinates. In this talk we will present the construction of a suitable generalized wave gauge in which our system has a "cubic weak null structure",which allows for the proof of global existence. 