Capillary Christoffel-Minkowski problem

2025/04/12 by Hu, Yingxiang, Ivaki, Mohammad N., Scheuer, Julian · 4 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2504.09320

Abstract

The result of Guan and Ma (Invent. Math. 151 (2003)) states that if ϕ^-1/k : \mathbbSⁿ → (0,∞) 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∈(0,π/2): if ϕ^-1/k : C_θ → (0,∞) is a capillary function and spherically convex, then ϕ is the σ_k curvature of a strictly convex capillary hypersurface.

Cited by

• Prescribed L_p curvature problem for convex capillary hypersurface
• The L_p dual Minkowski problem for capillary hypersurfaces
• The capillary Orlicz-Minkowski problem
• Capillary L_p Minkowski Flows

Related

• The capillary Christoffel-Minkowski problem
• Prescribed L_p curvature problem for convex capillary hypersurface
• The L_p dual Minkowski problem for capillary hypersurfaces
• Convex capillary hypersurfaces of prescribed curvature problem
• The capillary L_p-Minkowski problem