Alexandrov-Fenchel type inequalities with convex weight in space forms
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911583010029568 |
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| author | Kwong, Kwok-Kun Wei, Yong |
| author_facet | Kwong, Kwok-Kun Wei, Yong |
| contents | In this paper, we derive new sharp weighted Alexandrov-Fenchel and Minkowski inequalities for smooth, closed hypersurfaces under various convexity assumptions in Euclidean, spherical, and hyperbolic spaces. These inequalities extend classical results by incorporating weights given by convex, non-decreasing positive functions, which are otherwise arbitrary. Our approach gives rise to a broad family of geometric inequalities, as each convex, non-decreasing function yields a corresponding inequality, providing considerable flexibility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Alexandrov-Fenchel type inequalities with convex weight in space forms Kwong, Kwok-Kun Wei, Yong Differential Geometry Analysis of PDEs In this paper, we derive new sharp weighted Alexandrov-Fenchel and Minkowski inequalities for smooth, closed hypersurfaces under various convexity assumptions in Euclidean, spherical, and hyperbolic spaces. These inequalities extend classical results by incorporating weights given by convex, non-decreasing positive functions, which are otherwise arbitrary. Our approach gives rise to a broad family of geometric inequalities, as each convex, non-decreasing function yields a corresponding inequality, providing considerable flexibility. |
| title | Alexandrov-Fenchel type inequalities with convex weight in space forms |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2412.08923 |