The $L_p$ dual Minkowski problem for capillary hypersurfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918285292863488 |
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| author | Gao, Ya |
| author_facet | Gao, Ya |
| contents | In this paper, we consider the $L_p$ dual Minkowski problem for capillary hypersurfaces for $p>q$ and $q\leq 1$, which aims to find a capillary convex body with a prescribed capillary $(p,q)$-th dual curvature measure in the Euclidean half-space. We reduce it to a Monge-Ampère type equation with a Robin boundary condition on the unit spherical cap, we prove that there exists a unique smooth solution that solves this problem provided $θ\in (0,\fracπ{2})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $L_p$ dual Minkowski problem for capillary hypersurfaces Gao, Ya Differential Geometry Analysis of PDEs In this paper, we consider the $L_p$ dual Minkowski problem for capillary hypersurfaces for $p>q$ and $q\leq 1$, which aims to find a capillary convex body with a prescribed capillary $(p,q)$-th dual curvature measure in the Euclidean half-space. We reduce it to a Monge-Ampère type equation with a Robin boundary condition on the unit spherical cap, we prove that there exists a unique smooth solution that solves this problem provided $θ\in (0,\fracπ{2})$. |
| title | The $L_p$ dual Minkowski problem for capillary hypersurfaces |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2510.12804 |