单位球中具有毛细边界的平均曲率型流
微分几何
2026-02-19 v2 偏微分方程分析
摘要
本文研究了单位球中具有毛细边界的平均曲率型流。我们的流保持超曲面所围有界域的体积，并单调减小一个能量泛函。我们证明了其具有长时间存在性且子收敛于球冠。作为一个应用，我们解决了一个关于具有毛细边界的超曲面的等周问题。
引用
@article{arxiv.2001.03118,
title = {A mean curvature type flow with capillary boundary in a unit ball},
author = {Guofang Wang and Liangjun Weng},
journal= {arXiv preprint arXiv:2001.03118},
year = {2026}
}
备注
28 pages with some revisions: typos are corrected, rewrite Section 2.2, notations are unified and presentations are simplified. To appear in Calc. Var. Partial Differential Equations