Differential Geometry Seminar: Regina Rotman (University of Toronto), 'Short geodesic segments on closed Riemannian manifolds'

Event Date: 

Friday, March 15, 2013 -
3:00pm to 4:00pm

Event Location: 

  • 6635 South Hall

Event Contact: 

Guofang Wei
Email: wei@math.ucsb.edu

Abstract: A well-known result of J. P. Serre states that for an arbitrary pair of points on a closed Riemannian manifold there exist infinitely many geodesics connecting these points.

A natural question is whether one can estimate the length of the "k-th" geodesic in terms of the diameter of a manifold. We will demonstrate that given any pair of points p, q on a closed Riemannian manifold of dimension n and diameter d, there always exist at least k geodesics of length at most 4nk^2d connecting them.

We will also demonstrate that for any two points of a manifold that is diffeomorphic to the 2-sphere there always exist at least k geodesics between them of length at most 22kd. (Joint with A. Nabutovsky)