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- W4310001866 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 $tnearrowinfty$: (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 $gamma$." @default.
- W4310001866 created "2022-11-30" @default.
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- W4310001866 date "2020-01-04" @default.
- W4310001866 modified "2023-10-16" @default.
- W4310001866 title "On the precise asymptotics of Type-IIb solutions to mean curvature flow" @default.
- W4310001866 doi "https://doi.org/10.48550/arxiv.2001.02123" @default.
- W4310001866 hasPublicationYear "2020" @default.
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