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arXiv · 2509.10859

The capillary Orlicz-Minkowski problem

Xudong Wang·Baocheng Zhu
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Abstract

In this paper, we introduce a Robin boundary analogue of the Orlicz-Minkowski problem, which seeks to find a capillary convex body with a prescribed capillary Orlicz surface area measure in the upper Euclidean half-space. We obtain the volume-normalized smooth solutions to the capillary even Orlicz-Minkowski problem by the continuity method. In addition, we also establish a capillary Orlicz-Brunn-Minkowski inequality and a capillary Orlicz-Minkowski inequality, which can change our solutions to a spherical cap under some conditions.

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Xudong Wang, Baocheng Zhu. 2025-09-13. The capillary Orlicz-Minkowski problem. https://arxiv.org/abs/2509.10859

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