Stability of the cone-volume measure with near constant density
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913915196145664 |
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| author | Hu, Yingxiang Ivaki, Mohammad N. |
| author_facet | Hu, Yingxiang Ivaki, Mohammad N. |
| contents | We prove that if the density of the cone-volume measure of a smooth, strictly convex body with respect to the spherical Lebesgue measure is nearly constant, then a homothetic copy of the body is close to the unit ball in the $L^2$-distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06172 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of the cone-volume measure with near constant density Hu, Yingxiang Ivaki, Mohammad N. Differential Geometry Analysis of PDEs Metric Geometry We prove that if the density of the cone-volume measure of a smooth, strictly convex body with respect to the spherical Lebesgue measure is nearly constant, then a homothetic copy of the body is close to the unit ball in the $L^2$-distance. |
| title | Stability of the cone-volume measure with near constant density |
| topic | Differential Geometry Analysis of PDEs Metric Geometry |
| url | https://arxiv.org/abs/2408.06172 |