Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary II
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916758089105408 |
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| author | Mei, Xinqun Wang, Guofang Weng, Liangjun Xia, Chao |
| author_facet | Mei, Xinqun Wang, Guofang Weng, Liangjun Xia, Chao |
| contents | In this paper, we provide an affirmative answer to [16, Conjecture 1.5] on the Alexandrov-Fenchel inequality for quermassintegrals for convex capillary hypersurfaces in the Euclidean half-space. More generally, we establish a theory for capillary convex bodies in the half-space and prove a general Alexandrov-Fenchel inequality for mixed volumes of capillary convex bodies. The conjecture [16, Conjecture 1.5] follows as its consequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13655 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary II Mei, Xinqun Wang, Guofang Weng, Liangjun Xia, Chao Metric Geometry Spectral Theory Primary: 52A39. Secondary: 52A40, 53C24, 58J50 In this paper, we provide an affirmative answer to [16, Conjecture 1.5] on the Alexandrov-Fenchel inequality for quermassintegrals for convex capillary hypersurfaces in the Euclidean half-space. More generally, we establish a theory for capillary convex bodies in the half-space and prove a general Alexandrov-Fenchel inequality for mixed volumes of capillary convex bodies. The conjecture [16, Conjecture 1.5] follows as its consequence. |
| title | Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary II |
| topic | Metric Geometry Spectral Theory Primary: 52A39. Secondary: 52A40, 53C24, 58J50 |
| url | https://arxiv.org/abs/2408.13655 |