On the Type IIb solutions to mean curvature flow

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 R n , n ≥ 2 , satisfying there exist positive constants ϵ, c and N such that u ′ ( r ) ≥ c r ϵ for r ≥ 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 δ-Andrews' noncollapsing condition is translating soliton.