Blow-up Continuity for Type-I, Mean-Convex Mean Curvature Flow

2017/03/07 by Sonnanburg, Kevin
#53C44 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.02619

Abstract

Under mean curvature flow, a closed, embedded hypersurface M(t) becomes singular in finite time. For certain classes of mean-convex mean curvature flows, we show the continuity of the first singular time T and the limit set "M(T)", with respect to initial data. We employ an Angenent-like neck-pinching argument to force singularities in nearby flows. However, since we cannot prescribe initial data, we combine Andrews' α-non-collapsed condition and Colding and Minicozzi's uniqueness of tangent flows to place appropriately sized spheres in the region inside the hypersurface.

Related

• Singularity Profile in the Mean Curvature Flow
• Mean curvature blow up in mean curvature flow
• Blow Up of Compact Mean Curvature Flow Solutions with Bounded Mean Curvature
• The extension problem of the mean curvature flow (I)
• On the Mean Curvature Flow for σ_k-Convex Hypersurfaces