论文标题
在球中凸出毛细血管超曲面的平均曲率流动上
On the mean curvature type flow for convex capillary hypersurfaces in the ball
论文作者
论文摘要
在本文中，我们研究了带有毛细管边界的单位欧几里得球中超曲面的平均曲率流动，这是Wang-Xia和Wang-Weng引入的。我们表明，如果最初的Hypersurface严格凸出，则该流的解决方案严格凸出$ t> 0 $，在所有正时都存在，并平稳地收敛到球形盖。作为一种应用，我们证明了一个新的Alexandrov-Fenchel不平等的家族，用于具有毛细管边界的欧几里得球中凸出的凸出。
In this paper, we study the mean curvature type flow for hypersurfaces in the unit Euclidean ball with capillary boundary, which was introduced by Wang-Xia and Wang-Weng. We show that if the initial hypersurface is strictly convex, then the solution of this flow is strictly convex for $t>0$, exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a family of new Alexandrov-Fenchel inequalities for convex hypersurfaces in the unit Euclidean ball with capillary boundary.
