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Boundary and lens rigidity for non-convex manifolds

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Boundary and lens rigidity for non-convex manifolds
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13
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CC Attribution 3.0 Unported:
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We show that the boundary distance function determine a simply connected surface with no conjugate points and that the lens data determine a non-trapping surface with no conjugate points. The novelty is that the manifold is not assumed to be « simple », i.e the boundary is not assumed convex. We also show new result on the geodesic ray transform when there is trapped set. This is joint work with Mazzucchelli and Tzou.
CurveLengthPoint (geometry)Numerical digitMultiplication signManifoldBoundary value problemConjugacy classConvex setDistanceMatrix (mathematics)SurfaceAnalytic setStudent's t-testGenerating set of a groupComputer programmingDimensional analysisGeometryCategory of beingFunctional (mathematics)BuildingFamilyCondition numberMusical ensembleLipschitz-StetigkeitBeta functionNetwork topologyModulformAreaPower (physics)Inverse problemTheoremMetric systemGeodesicCounterexampleMathematicianAnalytic continuationIdentical particlesPrime idealLecture/Conference
MathematicsMKS system of unitsResultantNetwork topologyManifoldPoint (geometry)Condition numberFiber bundleState of matterTime domainConnected spaceMathematicianSocial classMultiplication signConvex setDimensional analysisCurvatureProof theoryMathematical analysisSet theoryComputer programmingBoundary value problemNumerical analysisGeometryConjugacy classObject (grammar)Metrischer RaumClosed setMany-sorted logicExtension (kinesiology)Negative numberArrow of timeFunctional (mathematics)DistanceLogical constantBeta functionEinbettung <Mathematik>Symmetric spaceGeodesicMetric systemSign (mathematics)DiffeomorphismLecture/Conference
Grand Unified TheoryTangent spaceGeodesicVector fieldMultiplication signSigma-algebraMaß <Mathematik>ExistenceTangentSet theoryMass flow rateCombinatory logicPoint (geometry)Direction (geometry)Boundary value problemManifoldMaxima and minimaTime domainProof theoryDistanceAngleDimensional analysisPrime idealFood energyTheory of everythingTrajectoryCategory of beingElement (mathematics)EllipseObject (grammar)Position operatorTerm (mathematics)Musical ensembleLine (geometry)Binary treeScatteringLecture/Conference
ManifoldTheoremConjugacy classMultiplication signBoundary value problemNetwork topologyCountingConformal mapFunctional (mathematics)Point (geometry)DistanceAreaAnalytic setSigma-algebraStiff equationLengthSpectrum (functional analysis)ScatteringCondition numberMass flow rateDifferent (Kate Ryan album)Goodness of fitSocial classParameter (computer programming)Propositional formulaDimensional analysisCounterexampleUniqueness quantificationSpline (mathematics)DivisorEquivalence relationPhysical systemProof theoryResultantAnalytic continuationGame theoryDrop (liquid)InfinityGlattheit <Mathematik>Maxima and minimaGeodesicLecture/Conference
Functional (mathematics)DistanceBoundary value problemNeighbourhood (graph theory)GeodesicPoint (geometry)OscillationScatteringProjective planeTransverse waveLemma (mathematics)Theory of relativityVector spaceGradientSigma-algebraSet theorySpacetimeMany-sorted logicTangentTime domainDimensional analysisLengthCurveTangent spaceDreiecksungleichungRight angleBeta functionReal numberTwo-dimensional spacePrime idealDivisorSocial classConjugacy classProof theoryConservation lawGastropod shellConvex setCategory of beingLecture/Conference
Compact spaceMultiplication signResultantTheoremBoundary value problemConjugacy classPoint (geometry)Equivalence relationCurvatureDimensional analysisStrategy gameNegative numberCondition numberScatteringMatrix (mathematics)Beta functionExistenceRight angleLecture/Conference
Multiplication signAlgebraic closureLengthHyperbolischer RaumStrategy gameHeegaard splittingConnected spaceGeodesicInfinity1 (number)Cylinder (geometry)Transformation (genetics)Boundary value problemPoint (geometry)Set theoryManifoldSocial classInvariant (mathematics)Functional (mathematics)Quantum stateAlgebraic structureMass flow rateCondition numberTheoremSurfaceConvex setSigma-algebraExistenceAnalytic setDirection (geometry)DiffeomorphismCurvatureSubsetLink (knot theory)MetreTerm (mathematics)Maß <Mathematik>Glattheit <Mathematik>Tournament (medieval)Thermodynamisches SystemEqualiser (mathematics)Basis <Mathematik>DivisorMortality rateOperator (mathematics)ResultantStability theorySpectrum (functional analysis)Observational studyDeterminantLecture/Conference
Stochastic kernel estimationTheoremFunctional (mathematics)Boundary value problemInfinityOperator (mathematics)Strategy gameThermodynamisches SystemDistribution (mathematics)Algebraic structurePopulation densityCategory of beingDynamical systemModulformGeodesicGlattheit <Mathematik>MeasurementMass flow rateMultiplication signPoint (geometry)ExistenceFinitismusLengthMaxima and minimaOrder (biology)Direction (geometry)AverageCanonical ensembleINTEGRALDerivation (linguistics)Exponential functionAntiderivativeReal numberProof theoryLinear mapNatural numberLecture/Conference
Food energyRing (mathematics)Time domainGeodesicWell-formed formulaConjugacy classOperator (mathematics)Identical particlesMereologyLaplace-OperatorBoundary value problemStability theoryPower (physics)Convex setNormal operatorDynamical systemPoint (geometry)TrajectoryGlattheit <Mathematik>Roundness (object)Self-adjoint operatorTerm (mathematics)Strategy gameInversion (music)Mass flow rateEstimatorTheoremRange (statistics)Dimensional analysisTransformation (genetics)HyperplaneCurveCounterexampleProof theoryCategory of beingTransverse waveEllipseDirection (geometry)InjektivitätHyperbolischer RaumLecture/Conference
ResultantFunctional (mathematics)ManifoldParameter (computer programming)Mathematical optimizationMultiplication signInfinityDivisorDistanceAnalytic setLecture/Conference
Parameter (computer programming)Boundary value problemSocial classDistanceGeodesicDivisorLecture/Conference
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