The extension problem of the mean curvature flow (I)

Abstract

We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in R^3.

45 pages, 4 figures, modified according to the suggestion of the referee report

References in corpus (2)

• Remarks of weak-compactness along Kahler Ricci flow
• Geometry of Two-dimensional Self-shrinkers

Cited by in corpus (3)

• Complete translating solitons to the mean curvature flow in ${\mathbb{R}}^3$ with nonnegative mean curvature
• Extension of two-dimensional mean curvature flow with free boundary
• Analysis of Vel$\acute{a}$zquez's solution to the mean curvature flow with a type $\mathrm{II}$ singularity