论文标题
半空间中凸毛细管超曲面的全部Alexandrov-Fenchel不平等系列
A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space
论文作者
论文摘要
在本文中，我们研究了半空间中高空的局部约束逆向曲率流，并具有$θ$ - 毛细血管边界，该边界最近由Wang-Weng-Xia引入。假设最初的高度表面是严格凸出的，其接触角$θ\在（0，π/2] $中。我们证明，流动的解决方案仍然是$ t> 0 $的严格凸起，在所有积极的时间内都存在，并顺利地收敛到球形上限。接触角$θ\ in（0，π/2] $。沿证明，我们为紧凑型歧管上的抛物线方程开发了新的张量最大原理，并具有适当的neumann边界条件。
In this paper, we study the locally constrained inverse curvature flow for hypersurfaces in the half-space with $θ$-capillary boundary, which was recently introduced by Wang-Weng-Xia. Assume that the initial hypersurface is strictly convex with the contact angle $θ\in (0,π/2]$. We prove that the solution of the flow remains to be strictly convex for $t>0$, exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space with the contact angle $θ\in(0,π/2]$. Along the proof, we develop a new tensor maximum principle for parabolic equations on compact manifold with proper Neumann boundary condition.
