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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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2016 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147734 |
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| 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147734 |
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dspace |
| spelling |
irk-123456789-1477342019-02-16T01:23:47Z The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions Sabau, S.V. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147734 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Sabau, S.V. |
| spellingShingle |
Sabau, S.V. The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Sabau, S.V. |
| author_sort |
Sabau, S.V. |
| title |
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_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_sort |
co-points of rays are cut points of upper level sets for busemann functions |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147734 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT sabausv thecopointsofraysarecutpointsofupperlevelsetsforbusemannfunctions AT sabausv copointsofraysarecutpointsofupperlevelsetsforbusemannfunctions |
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2023-05-20T17:28:10Z |
| last_indexed |
2023-05-20T17:28:10Z |
| _version_ |
1796153363955449856 |