The capillary $L_p$-Minkowski problem
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909615564783616 |
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| author | Mei, Xinqun Wang, Guofang Weng, Liangjun |
| author_facet | Mei, Xinqun Wang, Guofang Weng, Liangjun |
| contents | This paper is a continuation of our recent work [54] concerning the capillary Minkowski problem. We propose, in this paper, a capillary $L_p$-Minkowski problem for $p\geq 1$, which seeks to find a capillary convex body with a prescribed capillary $L_p$-surface area measure in the Euclidean half-space. This formulation provides a natural Robin boundary analogue of the classical $L_p$-Minkowski problem introduced by Lutwak [43]. For $p>1$, we resolve the capillary $L_p$-Minkowski problem in the smooth category by reducing it to a Monge-Ampère equation with a Robin boundary condition on the unit spherical cap. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_07746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The capillary $L_p$-Minkowski problem Mei, Xinqun Wang, Guofang Weng, Liangjun Differential Geometry Analysis of PDEs This paper is a continuation of our recent work [54] concerning the capillary Minkowski problem. We propose, in this paper, a capillary $L_p$-Minkowski problem for $p\geq 1$, which seeks to find a capillary convex body with a prescribed capillary $L_p$-surface area measure in the Euclidean half-space. This formulation provides a natural Robin boundary analogue of the classical $L_p$-Minkowski problem introduced by Lutwak [43]. For $p>1$, we resolve the capillary $L_p$-Minkowski problem in the smooth category by reducing it to a Monge-Ampère equation with a Robin boundary condition on the unit spherical cap. |
| title | The capillary $L_p$-Minkowski problem |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2505.07746 |