Pengzi Miao (University of Miami)

Title: Boundary effect of scalar curvature

Abstract: Manifolds with nonnegative scalar curvature arise naturally as maximal slices of physical spacetimes in general relativity. When the manifold is noncompact, there are the Riemannian positive mass theorem and Penrose inequality which give global results on how scalar curvature affects the manifold geometry near infinity. When the manifold is compact, it models bounded domains in such spacetime slices and how the scalar curvature affects its boundary geometry is tied to the quasi-local mass problem. In this talk, I will survey known results on boundary behavior of compact manifolds with nonnegative scalar curvature, and if time permits, I will discuss related open questions.