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arXiv · 1911.07282

Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up. II

James Isenberg·Haotian Wu·Zhou Zhang
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Abstract

We continue the study, initiated by the first two authors in \cite{IW19}, of Type-II curvature blow-up in mean curvature flow of complete noncompact embedded hypersurfaces. In particular, we construct mean curvature flow solutions, in the rotationally symmetric class, with the following precise asymptotics near the "vanishing" time $T$: (1) The highest curvature concentrates at the tip of the hypersurface (an umbilical point) and blows up at the rate $(T-t)^{-1}$. (2) In a neighbourhood of the tip, the solution converges to a translating soliton known as the bowl soliton. (3) Near spatial infinity, the hypersurface approaches a collapsing cylinder at an exponential rate.

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James Isenberg, Haotian Wu, Zhou Zhang. 2019-11-14. Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up. II. https://arxiv.org/abs/1911.07282

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