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arXiv · 2609.37258

The capillary $L_{p}$ dual Christoffel-Minkowski problem for $1<p<q\leq k+1$ with $1\leq k\leq n$

Guanghan Li·Mengliang Liu
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Abstract

This paper is concerned with a capillary $L_p$ Christoffel--Minkowski-type problem involving the prescription of a class of $L_p$ geometric measures formed by the $k$-th capillary area measure and the $q$-th dual curvature measure. By establishing a gradient estimate, we prove the existence of an even, smooth, strictly convex solution in the parameter range $1<p<q\leq k+1$, where $1\leq k\leq n$.

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Guanghan Li, Mengliang Liu. 2026-09-29. The capillary $L_{p}$ dual Christoffel-Minkowski problem for $1<p<q\leq k+1$ with $1\leq k\leq n$. https://arxiv.org/abs/2609.37258

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