Bounding Shortest Closed Geodesics with Diameter on compact 2-dimensional Orbifolds Homeomorphic to $S^2$
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911721916989440 |
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| author | Chen, Jinxuan |
| author_facet | Chen, Jinxuan |
| contents | Length-bounded sweepouts provide a method for bounding the length of the shortest closed geodesic of a closed manifold. In this paper, we generalize this approach to the case of compact 2-dimensional orbifolds homeomorphic to S^2 as well as compact 2-dimensional orbifolds with finite orbifold fundamental groups. We establish an inequality for the length of the shortest closed orbifold geodesic in terms of the diameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02781 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounding Shortest Closed Geodesics with Diameter on compact 2-dimensional Orbifolds Homeomorphic to $S^2$ Chen, Jinxuan Differential Geometry Metric Geometry Length-bounded sweepouts provide a method for bounding the length of the shortest closed geodesic of a closed manifold. In this paper, we generalize this approach to the case of compact 2-dimensional orbifolds homeomorphic to S^2 as well as compact 2-dimensional orbifolds with finite orbifold fundamental groups. We establish an inequality for the length of the shortest closed orbifold geodesic in terms of the diameter. |
| title | Bounding Shortest Closed Geodesics with Diameter on compact 2-dimensional Orbifolds Homeomorphic to $S^2$ |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2406.02781 |