Every closed surface of genus at least 18 is Loewner
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 clo...
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| Main Authors | , |
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| Format | Journal Article |
| Language | English |
| Published |
01.01.2024
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Li, Qiongling Su, Weixu |
| Author_xml | – sequence: 1 givenname: Qiongling surname: Li fullname: Li, Qiongling – sequence: 2 givenname: Weixu surname: Su fullname: Su, Weixu |
| BackLink | https://doi.org/10.48550/arXiv.2401.00720$$DView paper in arXiv |
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| Snippet | 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... |
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| SubjectTerms | Mathematics - Differential Geometry Mathematics - Geometric Topology |
| Title | Every closed surface of genus at least 18 is Loewner |
| URI | https://arxiv.org/abs/2401.00720 |
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