Singular Perturbations of Mean Curvature Flow

2004/07/19 by Giovanni Bellettini, Bellettini, Giovanni, Carlo Mantegazza +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG #msc:35K55 #msc:53A07 #msc:53C44

paper · pdf · doi:10.48550/arxiv.math/0407325

arxiv created 2004/07/19 · arxiv updated 2009/12/01

Abstract

We introduce a regularization method for mean curvature flow of a submanifold of arbitrary codimension in the Euclidean space, through higher order equations. We prove that the regularized problems converge to the mean curvature flow for all times before the first singularity.

Related

• Mean curvature flow in higher codimension
• The mean curvature flow of submanifolds of high codimension
• Singularity Models for High Codimension Mean Curvature Flow in Riemannian Manifolds
• Mean curvature flow of higher codimension in Riemannian manifolds
• Mean Curvature Flow of Higher Codimension in Hyperbolic Spaces