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arXiv · 2209.13516

A Minkowski-type inequality for capillary hypersurfaces in a half-space

Guofang Wang·Liangjun Weng·Chao Xia
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Abstract

In this article, we investigate a flow of inverse mean curvature type for capillary hypersurfaces in the half-space. We establish the global existence of solutions for this flow and demonstrate that it converges smoothly to a spherical cap as time tends to infinity. As a result, we derive a new Minkowski-type inequality for star-shaped and mean convex capillary hypersurfaces for the whole range of contact angle $\theta\in (0,\pi)$.

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Guofang Wang, Liangjun Weng, Chao Xia. 2022-09-27. A Minkowski-type inequality for capillary hypersurfaces in a half-space. https://doi.org/10.1016/j.jfa.2024.110496

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