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Capillary Christoffel-Minkowski problem

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arxiv 2504.09320 v1 pith:IO4QLIV3 submitted 2025-04-12 math.DG math.APmath.MG

Yingxiang Hu , Mohammad N. Ivaki , Julian Scheuer This is my paper · ORCID
classification math.DGmath.APmath.MG
keywords capillaryconvexcurvaturefunctionhypersurfaceinftyresultsigma
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abstract

The result of Guan and Ma (Invent. Math. 151 (2003)) states that if $\phi^{-1/k} : \mathbb{S}^n \to (0,\infty)$ is spherically convex, then $\phi$ arises as the $\sigma_k$ 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 $\theta\in(0,\pi/2)$: if $\phi^{-1/k} : \mathcal{C}_{\theta} \to (0,\infty)$ is a capillary function and spherically convex, then $\phi$ is the $\sigma_k$ curvature of a strictly convex capillary hypersurface.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Capillary curvature images

    math.DG 2025-05 conditional novelty 8.0 of 10

    The authors solve the even capillary L_p-Minkowski problem for -n < p < 1, proving existence of smooth even capillary hypersurfaces with prescribed curvature in the half-space.

  2. Capillary $L_p$ Minkowski Flows

    math.AP 2025-09 conditional novelty 6.0 of 10

    Anisotropic capillary Gauss curvature flows converge to smooth solutions of capillary L_p Minkowski problems for even data with p > -n-1 and for non-even data with p > n+1.

  3. The capillary Orlicz-Minkowski problem

    math.DG 2025-09 reject novelty 5.0 of 10

    The capillary Orlicz-Minkowski problem is formulated, but the main existence theorem is unsupported because the initial solution of the continuity method is not admissible under the paper's normalization.

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