Session S38 - Geometric Potential Analysis

Thursday, July 15, 20:10 ~ 20:40 UTC-3

On the Compactness of Poincare-Einstein manifolds

Fang Wang

Shanghai Jiao Tong University, China   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

I will talk about some recent progress on the compactness of Poincar\'{e}-Einstein manifolds and prove that once we get the compactness for one type of conformal compactification, then it also hold for some other type. We consider the conformal compactification with fixed smooth defining function and the adapted (including Fefferman-Graham) compactifications here. The main technique is an improved Schauder estimate for degenerate elliptic equations. This is joint work with Huihuang Zhou.

Joint work with Huihuang Zhou (Shanghai Jiao Tong University).

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