Uniqueness of solutions to a class of isotropic curvature problems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918077179887616 |
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| author | Ivaki, Mohammad N. Milman, Emanuel |
| author_facet | Ivaki, Mohammad N. Milman, Emanuel |
| contents | Employing a local version of the Brunn-Minkowski inequality, we give a new and simple proof of a result due to Andrews, Choi and Daskalopoulos that the origin-centred balls are the only closed, self-similar solutions of the Gauss curvature flow. Extensions to various non-linearities are obtained, assuming the centroid of the enclosed convex body is at the origin. By applying our method to the Alexandrov-Fenchel inequality, we also show that origin-centred balls are the only solutions to a large class of even Christoffel-Minkowski type problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_12839 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniqueness of solutions to a class of isotropic curvature problems Ivaki, Mohammad N. Milman, Emanuel Differential Geometry Analysis of PDEs Employing a local version of the Brunn-Minkowski inequality, we give a new and simple proof of a result due to Andrews, Choi and Daskalopoulos that the origin-centred balls are the only closed, self-similar solutions of the Gauss curvature flow. Extensions to various non-linearities are obtained, assuming the centroid of the enclosed convex body is at the origin. By applying our method to the Alexandrov-Fenchel inequality, we also show that origin-centred balls are the only solutions to a large class of even Christoffel-Minkowski type problems. |
| title | Uniqueness of solutions to a class of isotropic curvature problems |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2304.12839 |