A mean curvature type flow with capillary boundary in a unit ball
A mean curvature type flow with capillary boundary in a unit ball
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DOI：
10.1007/s00526-020-01812-7
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发表时间：
2020-01
影响因子：
2.1
通讯作者：
Guofang Wang;Liangjun Weng
中科院分区：
文献类型：
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作者：
Guofang Wang;Liangjun Weng
本文研究了单位球内具有毛细边界的平均曲率型流动。我们的流保持超曲面包围的有界域的体积，并单调减少能量functionalE。我们证明了它的长期存在性和次收敛于球冠。作为应用，我们解决了一类具有毛细边界的超曲面的等周问题。
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 functionalE. 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.