|Workshop on Geometric Functionals: Analysis and Applications|
|Topic:||Compactness of conformally compact Einstein manifolds in dimension 4|
|Date:||Monday, March 4|
|Time/Room:||10:00am - 11:00am/Simonyi Hall 101|
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.