The co-points are cut points of level sets for Busemann functions

Sorin V. Sabau

Published 2015-04-15Version 1

We show that the corays to a ray in a complete non-compact Finsler manifold contain geodesic segments to level sets of Busemann functions. Moreover, we characterize the set of co-points to a ray as the cut locus of such set levels. The structure theorem of the co-points set on a surface, namely that is a local tree, and other properties follows immediately from the known results about cut locus. We point out that our Main Theorems are new even for Riemannian manifolds.