Watch a 48-minute lecture from the General Relativity Workshop where University of Connecticut's Zhongshan An explores the fundamental problems in Riemannian geometry related to general relativity, specifically focusing on static vacuum Riemannian metrics with prescribed Bartnik data. Examine the basic properties of nonlinear and linearized static vacuum equations along with geometric boundary conditions, while learning about recent developments in the existence problem of static vacuum metrics. Delve into how static vacuum Riemannian metrics are essential for scalar curvature deformation and Einstein spacetime construction, with particular attention to the induced metric and mean curvature of the boundary. Gain insights from collaborative research conducted with Lan-Hsuan Huang on this significant geometric boundary value problem.