Math Seminars
R. Rotman
(PSU)
Curvature-free upper bounds for the length of stationary
objects
Let M be a closed Riemannian manifold of dimension n.
I will talk about curvature-free estimates for the length
of various minimal 1-dimensional objects, such as geodesic loops,
periodic geodesics, stationary geodesic nets and cycles and
the "kth'' geodesic segment between two points of M.
For example, I will show that at any point of M there exists a geodesic
loop of length less than or equal to 2nd, where d is the diameter of M.