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On the Type IIb solutions to mean curvature flow (1603.06102v8)
Published 19 Mar 2016 in math.DG
Abstract: In this paper we study the Type IIb mean curvature flow. We first prove that if the convex entire graph $(y,u(|y|))$ over $\mathbb{R}n$, $n\geq 2$, satisfying there exist positive constants $\epsilon$, $c$ and $N$ such that $ u'(r)\geq c r{\epsilon} $ for $r\geq N$, the longtime solution to mean curvature flow with initial data $(y,u(|y|))$ must be Type IIb. We also study the asymptotic behavior of Type IIb mean curvature flow and show that the limit of suitable rescaling sequence for mean-convex Type IIb mean curvature flow satisfying $\delta$-Andrews' noncollapsing condition is translating soliton.