论文标题
毛细血管边界半空间中凸出侧面的Alexandrov-Fenchel不平等现象
Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary
论文作者
论文摘要
在本文中，我们首先在半空间中引入了毛细血管超曲面的QuermassIntegrals。然后，我们解决了凸毛细血管超曲面的相关等级类型问题，并获得相应的Alexandrov-Fenchel不等式。为了证明这些结果，我们构建了一个新的局部约束曲率流，并证明该流量在全球范围内收敛到球形帽。
In this paper, we first introduce quermassintegrals for capillary hypersurfaces in the half-space. Then we solve the related isoperimetric type problems for the convex capillary hypersurfaces and obtain the corresponding Alexandrov-Fenchel inequalities. In order to prove these results, we construct a new locally constrained curvature flow and prove that the flow converges globally to a spherical cap.
