Abstract We continue the study, initiated by the first two authors in [15] , of Type-II curvature blow-up in mean curvature flow of complete noncompact hypersurfaces embedded in Euclidean space. In particular, we construct mean curvature flow solutions, in the rotationally symmetric class, with the following precise asymptotics near the “vanishing” time T: (1) The highest curvature concentrates at the tip of the hypersurface (an umbilical point) and blows up at the rate ( T − t ) − 1 . (2) In a neighbourhood of the tip, the solution converges to a translating soliton known as the bowl soliton. (3) Near spatial infinity, the hypersurface approaches a collapsing cylinder at an exponential rate.

中文翻译：

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具有 II 型曲率膨胀的非紧致超曲面的平均曲率流。二

摘要 我们继续研究 [15] 中前两位作者发起的关于嵌入欧几里得空间的完全非紧超曲面的平均曲率流中的 II 型曲率膨胀的研究。特别是，我们在旋转对称类中构建了平均曲率流解，在“消失”时间 T 附近具有以下精确渐近线：（1）最高曲率集中在超曲面的尖端（脐点）并爆炸以 ( T − t ) − 1 的速率。(2) 在尖端附近，解收敛到一个平移孤子，称为碗孤子。(3) 在空间无穷大附近，超曲面以指数速率接近一个坍缩的圆柱体。