The capillary Christoffel-Minkowski problem
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909053466181632 |
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| author | Mei, Xinqun Wang, Guofang Weng, Liangjun |
| author_facet | Mei, Xinqun Wang, Guofang Weng, Liangjun |
| contents | In this article, we introduce a $k$-th capillary area measure for capillary convex bodies in the Euclidean half-space, which serves as a boundary counterpart to the classical concept of area measure (see, e.g., \cite[Chapter 8]{Sch}). We then propose a Christoffel-Minkowski problem for capillary convex bodies, to find a capillary convex body in the Euclidean half-space with a prescribed $k$-th capillary area measure. This problem is equivalent to solving a Hessian-type equation with a Robin boundary value condition. We then establish the existence and uniqueness of a smooth solution under a natural sufficient condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16655 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The capillary Christoffel-Minkowski problem Mei, Xinqun Wang, Guofang Weng, Liangjun Analysis of PDEs Differential Geometry Primary: 53C21, 35J66. Secondary: 53C42, 53C45, 35J60 In this article, we introduce a $k$-th capillary area measure for capillary convex bodies in the Euclidean half-space, which serves as a boundary counterpart to the classical concept of area measure (see, e.g., \cite[Chapter 8]{Sch}). We then propose a Christoffel-Minkowski problem for capillary convex bodies, to find a capillary convex body in the Euclidean half-space with a prescribed $k$-th capillary area measure. This problem is equivalent to solving a Hessian-type equation with a Robin boundary value condition. We then establish the existence and uniqueness of a smooth solution under a natural sufficient condition. |
| title | The capillary Christoffel-Minkowski problem |
| topic | Analysis of PDEs Differential Geometry Primary: 53C21, 35J66. Secondary: 53C42, 53C45, 35J60 |
| url | https://arxiv.org/abs/2512.16655 |