GBU Geometric Analysis and PDE Seminar

host: Xumin Jiang, Zhehui Wang（王哲辉）

Title: Rigidity Theorem for Poincaré-Einstein Manifolds

Abstract: In this talk, I first introduce the classical rigidity theorem for Poincaré-Einstein manifold, which has conformal compactification in high regularity. Then I will report some recent rigidity result for Poincaré-Einstein manifold in the upper half plane model, which take the Euclidean space as its conformal infinity and whose adapted conformal metric has quadratic curvature decay at infinity. This is joint work with Sanghoon Lee (KIAS).



Title: Non-convexity of level sets of k-Hessian equations in convex ring

Abstract: In this talk, we will construct explicit examples that show the sublevel sets of the solution of a k-Hessian equation defined on a convex ring do not have to be convex. This is a joint work with Zhizhang Wang.