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arXiv · 2001.02123

On the precise asymptotics of Type-IIb solutions to mean curvature flow

James Isenberg·Haotian Wu·Zhou Zhang
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Abstract

In this paper, we study the precise asymptotics of noncompact Type-IIb solutions to the mean curvature flow. Precisely, for each real number $\gamma>0$, we construct mean curvature flow solutions, in the rotationally symmetric class, with the following precise asymptotics as $t\nearrow\infty$: (1) The highest curvature concentrates at the tip of the hypersurface (an umbilical point) and blows up at the Type-IIb rate $(2t+1)^{(\gamma-1)/2}$. (2) In a neighbourhood of the tip, the Type-IIb blow-up of the solution converges to a translating soliton known as the bowl soliton. (3) Near spatial infinity, the hypersurface has a precise growth rate depending on $\gamma$.

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James Isenberg, Haotian Wu, Zhou Zhang. 2020-01-05. On the precise asymptotics of Type-IIb solutions to mean curvature flow. https://arxiv.org/abs/2001.02123

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