Capillary Christoffel-Minkowski problem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913791055233024 |
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| author | Hu, Yingxiang Ivaki, Mohammad N. Scheuer, Julian |
| author_facet | Hu, Yingxiang Ivaki, Mohammad N. Scheuer, Julian |
| contents | The result of Guan and Ma (Invent. Math. 151 (2003)) states that if $ϕ^{-1/k} : \mathbb{S}^n \to (0,\infty)$ is spherically convex, then $ϕ$ arises as the $σ_k$ curvature (the $k$-th elementary symmetric function of the principal radii of curvature) of a strictly convex hypersurface. In this paper, we establish an analogous result in the capillary setting in the half-space for $θ\in(0,π/2)$: if $ϕ^{-1/k} : \mathcal{C}_θ \to (0,\infty)$ is a capillary function and spherically convex, then $ϕ$ is the $σ_k$ curvature of a strictly convex capillary hypersurface. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_09320 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Capillary Christoffel-Minkowski problem Hu, Yingxiang Ivaki, Mohammad N. Scheuer, Julian Differential Geometry Analysis of PDEs Metric Geometry The result of Guan and Ma (Invent. Math. 151 (2003)) states that if $ϕ^{-1/k} : \mathbb{S}^n \to (0,\infty)$ is spherically convex, then $ϕ$ arises as the $σ_k$ curvature (the $k$-th elementary symmetric function of the principal radii of curvature) of a strictly convex hypersurface. In this paper, we establish an analogous result in the capillary setting in the half-space for $θ\in(0,π/2)$: if $ϕ^{-1/k} : \mathcal{C}_θ \to (0,\infty)$ is a capillary function and spherically convex, then $ϕ$ is the $σ_k$ curvature of a strictly convex capillary hypersurface. |
| title | Capillary Christoffel-Minkowski problem |
| topic | Differential Geometry Analysis of PDEs Metric Geometry |
| url | https://arxiv.org/abs/2504.09320 |