Year: 2026
Type: article
Abstract: This paper is a continuation of our recent work [Adv. Math. 469 (2025), Paper No. 110230] concerning the capillary Minkowski problem. We propose, in this paper, a capillary $L_p$-Minkowski problem for $p\in \mathbb{R}$, which seeks to find a capillary convex body with a prescribed capillary $L_p$-surface area measure in the Euclidean half-space. This formulation provides a natural Robin boundary analogue of the classical $L_p$-Minkowski problem introduced by Lutwak [J. Differential Geom. 38 (1993), no. 1, 131--150]. For $p>1$, we resolve the capillary $L_p$-Minkowski problem in the smooth category by reducing it to a Monge--Ampère equation with a Robin boundary condition on the unit spherical cap.
DOI: 10.1090/tran/9866
Authors: Xinqun Mei, Guofang Wang, Liangjun Weng
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417517419