Modified Mean Curvature Flow in Fuchsian Manifolds

2026/07/22 by Yuk Shing Lam, Longzhi Lin
#math.DG #math.AP

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Abstract

In this paper, we show that the modified mean curvature flow starting from an arbitrary graph in a Fuchsian manifold exists for all time and converges smoothly to an equidistant surface of constant mean curvature as t→ ∞. This result generalizes earlier work to the modified mean curvature flow setting and removes the restrictive global gradient bound initially required for the standard mean curvature flow by Huang, Zhou, and the second author \citeHLZ2020.

Related

• Mean curvature flow in Fuchsian manifolds
• Modified mean curvature flow and CMC foliation conjecture in almost Fuchsian manifolds
• Mean curvature flow in higher codimension
• Mean curvature flow without singularities
• The mean curvature flow of submanifolds of high codimension