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Эта публикация цитируется в 3 научных статьях (всего 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.
Поступила: 7 августа 2015 г.; в окончательном варианте 6 апреля 2016 г.; опубликована 13 апреля 2016 г.
Образец цитирования:
Sorin V. Sabau, “The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions”, SIGMA, 12 (2016), 036, 12 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1118 https://www.mathnet.ru/rus/sigma/v12/p36
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