Prescribed $L_{p}$ curvature problem for convex capillary hypersurface
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918254964899840 |
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| author | Mei, Xinqun Wang, Guofang Weng, Liangjun |
| author_facet | Mei, Xinqun Wang, Guofang Weng, Liangjun |
| contents | We study the prescribed Lp curvature problem for convex capillary hypersurfaces in the Euclidean half-space. By reducing the problem to finding a convex solution of a Hessian quotient type equation with a Robin boundary condition on a spherical cap, we establish the existence and uniqueness of smooth admissible (in fact, strictly convex) solutions. As applications, we solve the capillary Lp Christoffel Minkowski problem in the smooth category, and we also obtain corresponding results for the prescribed Lp curvature problem and the related eigenvalue problem for convex capillary hypersurfaces in the Euclidean half-space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_16686 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prescribed $L_{p}$ curvature problem for convex capillary hypersurface Mei, Xinqun Wang, Guofang Weng, Liangjun Differential Geometry Primary: 58J05. Secondary: 52A20, 52A39 We study the prescribed Lp curvature problem for convex capillary hypersurfaces in the Euclidean half-space. By reducing the problem to finding a convex solution of a Hessian quotient type equation with a Robin boundary condition on a spherical cap, we establish the existence and uniqueness of smooth admissible (in fact, strictly convex) solutions. As applications, we solve the capillary Lp Christoffel Minkowski problem in the smooth category, and we also obtain corresponding results for the prescribed Lp curvature problem and the related eigenvalue problem for convex capillary hypersurfaces in the Euclidean half-space. |
| title | Prescribed $L_{p}$ curvature problem for convex capillary hypersurface |
| topic | Differential Geometry Primary: 58J05. Secondary: 52A20, 52A39 |
| url | https://arxiv.org/abs/2512.16686 |