Compactness of asymptotically hyperbolic Einstein manifolds in dimension 4 and applications 

• 主讲人：Yuxin Ge (University of toulouse 3)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2024-03-28 20:00 - 2024-03-28 21:00
• 地点： online

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Abstract: Given a closed riemannian manfiold of dimension 3 (M3,[h]), when will we fill in an asymp totically hyperbolic Einstein manifold of dimension 4 (X4,g+) such that r2g+|M = h on the boundary M = ∂X for some defining function r on X4? This problem is motivated by the correspondance AdS/CFT in quantum gravity proposed by Maldacena in 1998 et comes also from the study of the structure of asymptotically hyperbolic Einstein manifolds.

In this talk, I discuss the compactness issue of asymptotically hyperbolic Einstein manifolds in dimension 4, that is, how the compactness on conformal infinity leads to the compactness of the compactification of such manifolds under the suitable conditions on the topology and on some conformal invariants. As application, I discuss the uniqueness problem and non-existence result. It is based on the works with Alice Chang.

Bio: Yuxin Ge is a professor at University of toulouse 3.  He defended his doctoral thesis at l'Ecole normale superieure de Cachan  in 1997. His research mainly focuses on geometric analysis.