论文标题
约束的平均曲率流量和Alexandrov-Fenchel不等式
A constrained mean curvature flow and Alexandrov-Fenchel inequalities
论文作者
论文摘要
在本文中，我们研究了半空间中具有毛细血管边界的星形超曲面的局部约束平均曲率流。我们证明了它的长期存在以及全球融合到球形上限。此外，在\ cite {wwx2022}中定义的毛细血管Quermassintegrals沿流程沿流程进行单调演变，因此我们建立了一类新的Alexandrov-Fenchel不平等的新的Alexandrov-Fenchel不平等，用于半空间的capillary边界。
In this article, we study a locally constrained mean curvature flow for star-shaped hypersurfaces with capillary boundary in the half-space. We prove its long-time existence and the global convergence to a spherical cap. Furthermore, the capillary quermassintegrals defined in \cite{WWX2022} evolve monotonically along the flow, and hence we establish a class of new Alexandrov-Fenchel inequalities for convex hypersurfaces with capillary boundary in the half-space.
