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This article is cited in 3 scientific papers (total in 3 papers)
The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions
Sorin V. Sabau School of Science, Department of Mathematics, Tokai University, Sapporo 005–8600, Japan
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:
Finsler manifolds; ray; co-ray (asymptotic ray); cut locus; co-points; distance function; Busemann function.
Received: August 7, 2015; in final form April 6, 2016; Published online April 13, 2016
Citation:
Sorin V. Sabau, “The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions”, SIGMA, 12 (2016), 036, 12 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1118 https://www.mathnet.ru/eng/sigma/v12/p36
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