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arXiv · 2505.12921

Capillary curvature images

Yingxiang Hu·Mohammad N. Ivaki
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Abstract

In this paper, we solve the even capillary $L_p$-Minkowski problem for the range $-n < p < 1$ and $\theta \in (0,\frac{\pi}{2})$. Our approach is based on an iterative scheme that builds on the solution to the capillary Minkowski problem (i.e., the case $p = 1$) and leverages the monotonicity of a class of functionals under a family of capillary curvature image operators. These operators are constructed so that their fixed points, whenever they exist, correspond precisely to solutions of the capillary $L_p$-Minkowski problem.

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Yingxiang Hu, Mohammad N. Ivaki. 2025-05-19. Capillary curvature images. https://arxiv.org/abs/2505.12921

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