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

2023/11/07 by Huang, Zheng, Lin, Longzhi, Zhang, Zhou
#53C42 #57K32 #58J35 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2311.04298

Abstract

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 (∂ F)/(∂ t)=-(H-c)ν, which was first introduced by Xiao and the second named author in \citeLX12. As an application, we confirm Thurston's CMC foliation conjecture for such a subclass of almost Fuchsian manifolds.

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