Boundary effect of scalar curvature

Boundary effect of scalar curvature

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Pengzi Miao, University of Miami
Fine Hall 314

In this talk, we will discuss the effect of the scalar curvature of a Riemannian metric of a compact 3-manifold on the boundary geometry of the manifold. In particular, we will demonstrate that, on any compact Riemannian 3-manifold with nonnegative scalar curvature, if the boundary is a topological 2-sphere with nonnegative mean curvature, then the total mean curvature of the boundary is bounded from above by a constant depending only on the induced metric on the boundary. As an application, we propose a variational analogue of the Brow-York quasi-local mass functional in general relativity. This is a joint work with Christos Mantoulidis.