Report
A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space
| العنوان: | A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space |
|---|---|
| المؤلفون: | Hu, Yingxiang, Wei, Yong, Yang, Bo, Zhou, Tailong |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, 53C44, 53C21, 35K93, 52A40 |
| الوصف: | In this paper, we study the locally constrained inverse curvature flow for hypersurfaces in the half-space with $\theta$-capillary boundary, which was recently introduced by Wang-Weng-Xia. Assume that the initial hypersurface is strictly convex with the contact angle $\theta\in (0,\pi/2]$. 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 $\theta\in(0,\pi/2]$. Along the proof, we develop a new tensor maximum principle for parabolic equations on compact manifold with proper Neumann boundary condition. Comment: v2, 28 pages, 2 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2209.12479 |
| رقم الانضمام: | edsarx.2209.12479 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |