Equivariant wave maps on a class of rotationally symmetric manifolds

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Equivariant wave maps on a class of rotationally symmetric manifolds
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Joint work with Qidi Zhang (Shanghai). We study a class of rotationally invariant manifolds, which we call admissible, on which it is possible to prove smoothing and Strichartz estimates for the wave equation. This class includes asymptotically flat manifolds but also perturbations of real hyperbolic spaces \mathbb^ for n\ge3, and other manifolds with non vanishing curvature at infinity. Among other results we can prove the global existence of equivariant wave maps from admissible manifolds to general targets, for small initial data of critical regularity H^
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coefficient of inside and undecided and in effect but just a minute technicalities to prove some project estimates of the decision efficiency not the big problem you have with the work of harder for the higher the United States and and then you have to to read the result in the original court that's OK so you have to go back to them also want knowledge and then I mean that the address of the work is essentially to construct manifolds and we see how the hell out of the class it's just a better show you so this is a change according so that users to reduce the question To this form so I suggest you get stand up there with racial you imprison mentioned by 2 K which is nice because it gives system but the students instances but the properties the problem is that this potential his singular and a critic of the K and you know that if you will always the negative part of this city is too bad because to be give you lose everything so there's some part of risk here and also here essentially have just a here but they're not the intractable a began is so there is a yet bartender association which has been has been taken here and then you have a two-week but OK so this is a cubic Samina regression with Cingular coefficient so we chose which has the same critical spaces as usual and was and look at it such but this is what I just said that because of the skippers in OK this is just the kind of thing to see that the estimate with improve the full set of estimates with the exception again .period also in this case the South misunderstand us because the that just as the method the usual condition on the admissibility of the acute and this is the indigeneous version this is precisely the sort of estimates we've improved In in some coordinates as saying that you get someone somewhere OK mn let me briefly recall you that there is now an extensive literature on a status estimates and dispersal estimates and sloping estimates of the various perturbations on the stand questions so far 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