天美传媒

Wuhan University| 中文

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Published on 28 Nov 2025

The capillary Orlicz-Minkowski problem

In this talk, we introduce a Robin boundary analogue of the Orlicz-Minkowski problem, which seeks to characterize capillary convex bodies with prescribed capillary Orlicz surface area measures in the upper Euclidean half-space. By applying the continuity method, we establish the existence of smooth solutions to the capillary even Orlicz-Minkowski problem. In addition, we derive capillary Orlicz-Brunn-Minkowski and Orlicz-Minkowski inequalities, which, under suitable conditions, characterize spherical caps as the unique solutions.