BIRS Workshop Lecture Videos
Short geodesic segments on closed Riemannian manifolds Rotman, Regina
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 on a closed Riemannian manifold M of dimension n and diameter d, there always exist at least k geodesics of length at most 4nk2d 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).
Item Citations and Data
Attribution-NonCommercial-NoDerivs 2.5 Canada