The extension and convergence of mean curvature flow in higher codimension

2011/04/05 by Kefeng Liu, Hongwei Xu, Liu, Kefeng +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1104.0971

openalex publication_date 2011/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first investigate the integral curvature condition to extend the mean curvature flow of submanifolds in a Riemannian manifold with codimension d≥1, which generalizes the extension theorem for the mean curvature flow of hypersurfaces due to Le-Šešum \citeLS and the authors \citeXYZ1,XYZ2. Using the extension theorem, we prove two convergence theorems for the mean curvature flow of closed submanifolds in R^n+d under suitable integral curvature conditions.

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• Mean curvature flow of arbitrary codimension in complex projective spaces