Long-time existence of mean curvature flow with external force fields

2006/11/29 by Yanan Liu, Liu, Yanan, Huaiyu Jian +1 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.math/0611906

openalex publication_date 2006/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the evolution of submannifold moving by mean curvature minus a external force field. We prove that the flow has a long-time smooth solution for all time under almost optimal conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the external force field, with its any order derivatives, is bounded, and the field is convex with its eigenvalues satisfying a pinch inequality.

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• Harnack Inequality for f-Mean Curvature Flow
• Existence of martingale solutions for a stochastic weighted mean curvature flow of graphs

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