Estimates for the minimal length of various
1-dimensional stationary objects in Riemannian geometry
Rina Rotman
University of Toronto
November 27, 2006
Abstract: I will talk about
curvature-free estimates for the length of periodic geodesics, minimal
geodesic nets and geodesic loops at each point of a closed Riemannian
manifold M in terms of the
volume or in terms of the diameter of M. In particular, I will
show that at each point of M there exists a geodesic loop of length
less than or equal to 2nd, where n is the dimension and d is the
diameter of M.