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arXiv · 2311.04298

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

Zheng Huang·Longzhi Lin·Zhou Zhang
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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 $$\frac{\partial F}{\partial t}=-(H-c)\vecν,$$ 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.

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Zheng Huang, Longzhi Lin, Zhou Zhang. 2023-11-07. Modified mean curvature flow and CMC foliation conjecture in almost Fuchsian manifolds. https://arxiv.org/abs/2311.04298

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