The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2016
• Main Author: Sabau, S.V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147734
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions / S.V. Sabau // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 12 назв. — англ.

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 th...