Differential Geometry Seminar: A polyhedron comparison theorem for 3-manifolds with positive scalar curvature

Seminar | January 22 | 2:10-3 p.m. | 939 Evans Hall

 Chao Li, Stanford

 Department of Mathematics

We establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by Gromov. For a large collection of polyhedra with interior non-negative scalar curvature and mean convex faces, we prove that the dihedral angles along its edges cannot be everywhere less or equal than those of the corresponding Euclidean model, unless it is a isometric to a flat polyhedron.