A Characterization of the Singular Time of the Mean Curvature Flow

2010/05/24 by Cooper, Andrew A
#53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1005.4382

Abstract

In this note we investigate the behaviour at finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M^m_t\hookrightarrow (N^m+n, h). We show that they are characterized by the blow-up of a trace A = H ⋅ II of the square of the second fundamental form.

Related

• Mean curvature blow up in mean curvature flow
• Some extensions of the mean curvature flow in Riemannian manifolds
• A note on sigular time of mean curvature flow
• The mean curvature flow of submanifolds of high codimension
• The extension problem of the mean curvature flow (I)