报告题目：Compactness of Asymptotically Hyperbolic Einstein Manifolds in Dimension 4 and Applications

报告时间：2023-08-12  09:30-10:30

报告人：Prof.Yuxin Ge，University of Toulouse 3

报告地点：理学院东北楼四楼报告厅

Abstract：Given a closed Riemannian manifold of dimension 3(M³ ,[h]) , when will we fill in an asymptotically hyperbolic Einstein manifold of dimension 4(X⁴,g₊)  such that r²g₊|.. = 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.