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arXiv · 2001.03118

A mean curvature type flow with capillary boundary in a unit ball

Guofang Wang·Liangjun Weng
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Abstract

In this paper, we study a mean curvature type flow with capillary boundary in the unit ball. Our flow preserves the volume of the bounded domain enclosed by the hypersurface, and monotonically decreases an energy functional $E$. We show that it has the longtime existence and subconverges to spherical caps. As an application, we solve an isoperimetric problem for hypersurfaces with capillary boundary.

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Guofang Wang, Liangjun Weng. 2020-01-09. A mean curvature type flow with capillary boundary in a unit ball. https://doi.org/10.1007/s00526-020-01812-7

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