RUS  ENG
Полная версия
ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2016, том 12, 036, 12 стр. (Mi sigma1118)

Эта публикация цитируется в 3 статьях

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

Аннотация: 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.

Ключевые слова: Finsler manifolds; ray; co-ray (asymptotic ray); cut locus; co-points; distance function; Busemann function.

MSC: 53C60; 53C22

Поступила: 7 августа 2015 г.; в окончательном варианте 6 апреля 2016 г.; опубликована 13 апреля 2016 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2016.036



Реферативные базы данных:
ArXiv: 1504.03921


© МИАН, 2024