On the precise asymptotics of Type-IIb solutions to mean curvature flow
On the precise asymptotics of Type-IIb solutions to mean curvature flow
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DOI：
10.1090/btran/76
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发表时间：
2020-01
期刊：
影响因子：
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通讯作者：
J. Isenberg;Haotian Wu;Zuxun Zhang
中科院分区：
文献类型：
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作者：
J. Isenberg;Haotian Wu;Zuxun Zhang
本文研究了平均曲率流的非紧IIb型解的精确渐近性。精确地说，对于每一个真实的数$\gamma>0$，我们在旋转对称类中构造平均曲率流解，其精确渐近性为$t\nearrow\infty$：（1）最高曲率集中在超曲面的尖端（脐点），并以IIb型速率$（2 t +1）^{（\gamma-1）/2}$爆破。(2)在附近的尖端，IIb型爆破的解决方案收敛到一个翻译孤子称为碗孤子。(3)在空间无穷大附近，超曲面有一个精确的增长率，它依赖于$\gamma$。
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 $\gamma$.