凸古平均曲率流中的坍缩与非坍缩

IF 1.2 1区 数学 Q1 MATHEMATICS
T. Bourni, Mathew T. Langford, S. Lynch
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引用次数: 5

摘要

摘要给出了凸古平均曲率流中坍缩和非坍缩的几个特征,特别证明了当且仅当流渐近于至少一个Grim超平面时才会发生坍缩。因此,我们排除了在(n-1) {(n-1)} -凸平均曲率流中坍缩奇点模型(即使初始基准面仅浸入)。明确的反例表明(n-1) {(n-1)} -凸性是最优的。我们也能够排除坍缩奇点模型对于适当的高余维缩紧解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Collapsing and noncollapsing in convex ancient mean curvature flow
Abstract We provide several characterizations of collapsing and noncollapsing in convex ancient mean curvature flow, establishing in particular that collapsing occurs if and only if the flow is asymptotic to at least one Grim hyperplane. As a consequence, we rule out collapsing singularity models in ( n - 1 ) {(n-1)} -convex mean curvature flow (even when the initial datum is only immersed). Explicit counterexamples show that ( n - 1 ) {(n-1)} -convexity is optimal. We are also able to rule out collapsing singularity models for suitably pinched solutions of higher codimension.
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来源期刊
CiteScore
2.50
自引率
6.70%
发文量
97
审稿时长
6-12 weeks
期刊介绍: The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle"s Journal. In the almost 180 years of its existence, Crelle"s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI"s Journal Citation Report.
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