Modified mean curvature flow and CMC foliation conjecture in almost Fuchsian manifolds

Autor:	Huang, Zheng, Lin, Longzhi, Zhang, Zhou
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs Mathematics - Geometric Topology 53C42 58J35 57K32
Druh dokumentu:	Working Paper
Popis:	There has been a conjecture, often attributed to Thurston, which asserts that every almost Fuchsian manifold is foliated by closed incompressible constant mean curvature (CMC) surfaces. In this paper, for a certain class of almost Fuchsian manifolds, we prove the long-time existence and convergence of the modified mean curvature flow $$\frac{\partial F}{\partial t}=-(H-c)\vec{\nu},$$ which was first introduced by Xiao and the second named author in \cite{LX12}. As an application, we confirm Thurston's CMC foliation conjecture for such a subclass of almost Fuchsian manifolds. Comment: 49 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.04298 Zobrazit plný text záznamu View this record from Arxiv