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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.00720 |
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| _version_ | 1866913189337235456 |
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| author | Li, Qiongling Su, Weixu |
| author_facet | Li, Qiongling Su, Weixu |
| contents | In this paper, we obtain an improved upper bound involving the systole and area for the volume entropy of a Riemannian surface. As a result, we show that every orientable and closed Riemannian surface of genus $g\geq 18$ satisfies Loewner's systolic ratio inequality. We also show that every closed orientable and nonpositively curved Riemannnian surface of genus $g\geq 11$ satisfies Loewner's systolic ratio inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00720 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Every closed surface of genus at least 18 is Loewner Li, Qiongling Su, Weixu Differential Geometry Geometric Topology 53C23, 37C35 In this paper, we obtain an improved upper bound involving the systole and area for the volume entropy of a Riemannian surface. As a result, we show that every orientable and closed Riemannian surface of genus $g\geq 18$ satisfies Loewner's systolic ratio inequality. We also show that every closed orientable and nonpositively curved Riemannnian surface of genus $g\geq 11$ satisfies Loewner's systolic ratio inequality. |
| title | Every closed surface of genus at least 18 is Loewner |
| topic | Differential Geometry Geometric Topology 53C23, 37C35 |
| url | https://arxiv.org/abs/2401.00720 |