The capillary Orlicz-Minkowski problem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909786268762112 |
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| author | Wang, Xudong Zhu, Baocheng |
| author_facet | Wang, Xudong Zhu, Baocheng |
| contents | In this paper, we introduce a Robin boundary analogue of the Orlicz-Minkowski problem, which seeks to find a capillary convex body with a prescribed capillary Orlicz surface area measure in the upper Euclidean half-space. We obtain the volume-normalized smooth solutions to the capillary even Orlicz-Minkowski problem by the continuity method. In addition, we also establish a capillary Orlicz-Brunn-Minkowski inequality and a capillary Orlicz-Minkowski inequality, which can change our solutions to a spherical cap under some conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The capillary Orlicz-Minkowski problem Wang, Xudong Zhu, Baocheng Differential Geometry In this paper, we introduce a Robin boundary analogue of the Orlicz-Minkowski problem, which seeks to find a capillary convex body with a prescribed capillary Orlicz surface area measure in the upper Euclidean half-space. We obtain the volume-normalized smooth solutions to the capillary even Orlicz-Minkowski problem by the continuity method. In addition, we also establish a capillary Orlicz-Brunn-Minkowski inequality and a capillary Orlicz-Minkowski inequality, which can change our solutions to a spherical cap under some conditions. |
| title | The capillary Orlicz-Minkowski problem |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2509.10859 |