Nonpositively curved surfaces are Loewner
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866916310154215424 |
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| author | Katz, Mikhail G. Sabourau, Stephane |
| author_facet | Katz, Mikhail G. Sabourau, Stephane |
| contents | We show that every closed nonpositively curved surface satisfies Loewner's systolic inequality. The proof relies on a combination of the Gauss-Bonnet formula with an averaging argument using the invariance of the Liouville measure under the geodesic flow. This enables us to find a disk with large total curvature around its center yielding a large area. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonpositively curved surfaces are Loewner Katz, Mikhail G. Sabourau, Stephane Differential Geometry Primary 53C20, Secondary 53C23 We show that every closed nonpositively curved surface satisfies Loewner's systolic inequality. The proof relies on a combination of the Gauss-Bonnet formula with an averaging argument using the invariance of the Liouville measure under the geodesic flow. This enables us to find a disk with large total curvature around its center yielding a large area. |
| title | Nonpositively curved surfaces are Loewner |
| topic | Differential Geometry Primary 53C20, Secondary 53C23 |
| url | https://arxiv.org/abs/2404.00757 |