Static vacuum metrics with prescribed Bartnik boundary data

12.01.2023, 14:15-15:45  –  2.22 und Zoom
Geometric Analysis, Differential Geometry and Relativity

Zhongshan An

The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation, as well as constructing vacuum Einstein spacetimes. Existence of static  vacuum Riemannian metrics with prescribed Bartnik data — the induced metric and mean curvature of the boundary — is one of the most interesting problems in Riemannian geometry related to general relativity. It is also a problem on the global solvability of a natural geometric system of partial differential equations. In this talk I will present some recent progress towards the existence problem of static vacuum metrics based on joint works with Lan-Hsuan Huang.