Subsequent singularities of mean convex mean curvature flows in smooth manifolds

Abstract

For any $n$-dimensional smooth manifold $\Sigma$, we show that all the singularities of the mean curvature flow with any initial mean convex hypersurface in $\Sigma$ are cylindrical (of convex type) if the flow converges to a smooth hypersurface $M_{\infty }$ (maybe empty) at infinity. Previously this was shown (i) for $n\le 7$, and (ii) for arbitrary $n$ up to the first singular time without the smooth condition for $M_{\infty }$.

11 pages

References in corpus (2)

• Subsequent Singularities in Mean-Convex Mean Curvature Flow
• The translating soliton of mean curvature flow