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arXiv · 2405.02722

Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flow

Carlo Sinestrari·Liangjun Weng
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Abstract

In this paper, we introduce a volume- or area-preserving curvature flow for hypersurfaces with capillary boundary in the half-space, with speed given by a positive power of the mean curvature with a non-local averaging term. We demonstrate that for any convex initial hypersurface with a capillary boundary, the flow exists for all time and smoothly converges to a spherical cap as $t \to +\infty$

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Carlo Sinestrari, Liangjun Weng. 2024-05-04. Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flow. https://doi.org/10.1007/s00526-024-02838-x

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