The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions
Differential Geometry
2016-04-14 v3
Abstract
We show that the co-rays to a ray in a complete non-compact Finsler manifold contain geodesic segments to upper level sets of Busemann functions. Moreover, we characterise the co-point set to a ray as the cut locus of such level sets. The structure theorem of the co-point set on a surface, namely that is a local tree, and other properties follow immediately from the known results about the cut locus. We point out that some of our findings, in special the relation of co-point set to the upper lever sets, are new even for Riemannian manifolds.
Keywords
Cite
@article{arxiv.1504.03921,
title = {The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions},
author = {Sorin V. Sabau},
journal= {arXiv preprint arXiv:1504.03921},
year = {2016}
}