Compactness of conformally compact Einstein manifolds in dimension 4

Workshop on Geometric Functionals: Analysis and Applications
Topic:Compactness of conformally compact Einstein manifolds in dimension 4
Speaker:Alice Chang
Affiliation:Princeton University
Date:Monday, March 4
Time/Room:10:00am - 11:00am/Simonyi Hall 101
Video Link:https://video.ias.edu/workshop/2019/0304-AliceChang

Abstract:  Given a class of conformally compact Einstein manifolds with boundary, we are interested to study the compactness of the class under some local and non-local boundary constraints. I will report some joint work with Yuxin Ge and Jie Qing including compactness results which are improvements of the earlier conditions obtained by Chang-Ge and compactness results under perturbation conditions when the L2 norm of the Weyl curvature is small. As a by product, we will derive the global uniqueness of conformally compact Einstein metrics on the 4-Ball constructed in the earlier work of Graham-Lee.