The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions
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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2016 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147734 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862609509065687040 |
|---|---|
| author | Sabau, S.V. |
| author_facet | Sabau, S.V. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-28T20:11:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147734 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-28T20:11:05Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sabau, S.V. 2019-02-15T18:53:04Z 2019-02-15T18:53:04Z 2016 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. 1815-0659 2010 Mathematics Subject Classification: 53C60; 53C22 DOI:10.3842/SIGMA.2016.036 https://nasplib.isofts.kiev.ua/handle/123456789/147734 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. I am grateful to Professor M. Tanaka for bringing this topic into my attention and for many
 illuminating discussions. I am also deeply indebted to the anonymous referees for their constructive
 criticism and extremely useful suggestions that improved the manuscript enormously.
 Also I thank to N. Boonnam for reading an early version of the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions Article published earlier |
| spellingShingle | The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions Sabau, S.V. |
| title | The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions |
| title_full | The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions |
| title_fullStr | The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions |
| title_full_unstemmed | The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions |
| title_short | The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions |
| title_sort | co-points of rays are cut points of upper level sets for busemann functions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147734 |
| work_keys_str_mv | AT sabausv thecopointsofraysarecutpointsofupperlevelsetsforbusemannfunctions AT sabausv copointsofraysarecutpointsofupperlevelsetsforbusemannfunctions |