Prof. Miao Pengzi，University of Miami, USA

Scalar curvature is the simplest curvature invariant in Riemannian geometry. In general relativity, it relates to matter distribution along spacelike hypersurfaces in spacetimes. If the underlying manifold is noncompact, fundamental results on manifolds with nonnegative scalar curvature include the Riemannian positive mass theorem and the Riemannian Penrose inequality. In this talk, we discuss implications of those theorems to compact manifolds with boundary. More precisely, we seek to understand how nonnegative scalar curvature of a compact manifold influences the mean curvature of its boundary surface.