a polyhedron comparison theorem for 3manifolds with positive scalar curvature
a polyhedron comparison theorem for 3manifolds with positive scalar curvature

Chao Li, Stanford University
Fine Hall 314
We establish a comparison theorem for polyhedra in 3manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by Gromov. For a large collections of polyhedra with interior nonnegative scalar curvature and mean convex faces, we prove 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.