Wednesday, 09 April, 2014
SPEAKER: Prof. Ken Knox, UT
TITLE:Some geometric stability theorems in Riemannian geometry, Part 2
ABSTRACT: Rigidity theorems have a long history in Riemannian geometry. For example, long ago it was shown that the only convex body in Euclidean 3-space with spherical `intrinsic boundary' must be the unit ball. The proofs of the classical rigidity theorems, however, do not seem to generalize to `almost-rigidity' theorems: new techniques are required. In this talk, we will identify a few classical theorems regarding the rigidity of isometric immersions, and show how they can be turned into `stability theorems' within the class of Riemannian 3-manifolds with boundary.