A local isoperimetric inequality for balls with nonpositive curvature
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908840884174848 |
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| author | Ghomi, Mohammad Stavroulakis, John Ioannis |
| author_facet | Ghomi, Mohammad Stavroulakis, John Ioannis |
| contents | We show that small perturbations of the metric of a ball in Euclidean n-space to metrics with nonpositive curvature do not reduce the isoperimetric ratio. Furthermore, the isoperimetric ratio is preserved only if the perturbation corresponds to a homothety of the ball. These results establish a sharp local version of the Cartan-Hadamard conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11971 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A local isoperimetric inequality for balls with nonpositive curvature Ghomi, Mohammad Stavroulakis, John Ioannis Differential Geometry Metric Geometry We show that small perturbations of the metric of a ball in Euclidean n-space to metrics with nonpositive curvature do not reduce the isoperimetric ratio. Furthermore, the isoperimetric ratio is preserved only if the perturbation corresponds to a homothety of the ball. These results establish a sharp local version of the Cartan-Hadamard conjecture. |
| title | A local isoperimetric inequality for balls with nonpositive curvature |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2505.11971 |