On the extension to mean curvature flow in lower dimension

Abstract

In this paper, we prove that if $M_t\subset {\mathbb{R}}^{n+1}$, $2\le n\le 6$, is the $n$-dimensional closed embedded $\mathcal{F}-$stable solution to mean curvature flow with mean curvature of $M_t$ is uniformly bounded on $[0,T)$ for $T<\infty$, then the flow can be smoothly extended over time $T$.

6 pages, an error is corrected

References in corpus (1)

• Blow-up of the mean curvature at the first singular time of the mean curvature flow