Rina Rotman
University of Toronto
The length of a shortest closed geodesic and the minimal mass of a stationary 1-cycle.
Abstract:
Abstract: First, I will talk about upper bounds for the length of a shortest closed geodesic, l(M), involving different curvature bounds on a Riemannian manifold M. The process of obtaining those estimates involves constructing "optimal'' homotopies that connect contractible spheres with points. Then I will talk about the estimates for l(M), when M is diffeomorphic to the 2-dimensional sphere, and for the minimal mass of a stationary 1-cycle on an arbitrary manifold M. Those estimates are in terms of the volume or the diameter of M only.