Seminar| Institute of Mathematical Sciences
Time: Wednesday, December 24th, 2025,10:00-11:00
Location: RS408, IMS
Speaker: Zhongshan An, University of Science and Technology of China
Abstract: We will talk about existence of Einstein metrics on manifolds with boundary, while prescribing the induced conformal metric and mean curvature of the boundary. In dimension 3, this becomes finding conformal embeddings of surfaces into constant sectional curvature space forms, with prescribed mean curvature. We will show existence of such conformal embeddings near generic Einstein background. We will also discuss the existence question in higher dimensions, where things become more subtle and a stability boundary condition is used to construct metrics with nonpositive Einstein constant.