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.

中文翻译：

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单位球中具有毛细管边界的平均曲率型流

在本文中，我们研究了在单位球中具有毛细管边界的平均曲率型流动。我们的流保留由超曲面包围的有界域的体积，并单调地减少能量官能ë。我们证明它具有长期存在性，并且会聚到球形帽。作为一种应用，我们解决了带有毛细边界的超曲面的等渗问题。