Alex Nabutowsky, University of Toronto, November 18, 2002
Title: The shortest closed geodesic and stationary 1-cycles
Abstract:
How long is the shortest closed geodesic on a closed
Riemannian manifold? Jointly with Regina Rotman we proved that
if $M$ is diffeomorphic to the two-dimensional sphere then
the length $l(M)$ of the shortest closed geodesic on $M$ does not exceed
$8\sqrt{Area(M)}$. Also, we proved that in this case
$l(M)\le 4\ diameter(M)$.
In the general case, when $M$ is an arbitrary closed Riemannian manifold
we proved similar curvature-free bounds for the minimal mass of a
non-trivial stationary 1-cycle.