On the Type IIb solutions to mean curvature flow

[摘要] In this paper we study the Type IIb mean curvature flow. We first prove that if the convex entire graph (y, u(vertical bar y vertical bar )) over R-n , n >= 2, satisfying there exist positive constants is an element of, c and N such that u' (r) >= cr(epsilon); for r >= N , the longtime solution to mean curvature flow with initial data (y, u(vertical bar y vertical bar )) 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. (c) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-11-05

[关键词] Type IIb mean curvature flows;Entire graphs;Andrews' noncollapsing theorem for noncompact;hypersurfaces