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arXiv · 2209.12488

On the mean curvature type flow for convex capillary hypersurfaces in the ball

Yingxiang Hu·Yong Wei·Bo Yang·Tailong Zhou
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Abstract

In this paper, we study the mean curvature type flow for hypersurfaces in the unit Euclidean ball with capillary boundary, which was introduced by Wang-Xia and Wang-Weng. We show that if the initial hypersurface is strictly convex, then the solution of this flow is strictly convex for $t>0$, exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a family of new Alexandrov-Fenchel inequalities for convex hypersurfaces in the unit Euclidean ball with capillary boundary.

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Yingxiang Hu, Yong Wei, Bo Yang, Tailong Zhou. 2022-09-26. On the mean curvature type flow for convex capillary hypersurfaces in the ball. https://doi.org/10.1007/s00526-023-02554-y

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