论文标题
脖子奇点的稳定性
Stability of neckpinch singularities
论文作者
论文摘要
在本文中，我们研究了领带奇异性的稳定性。我们表明，如果平均曲率流$ \ {m_t \} $在第一个单一单数时只会产生许多颈钉奇点，那么在第一个单singular时，在任何足够小的$ m_0 $的小扰动中，平均曲率流也可以在任何足够小的$ m_0 $的小扰动开始。在上述意义上，我们还表现出非重型颈钉奇异性的稳定性，这表示支持I型奇异性的稳定性。
In this paper, we study the stability of neckpinch singularities. We show that if a mean curvature flow $\{M_t\}$ develops only finitely many neckpinch singularities at the first singular time, then the mean curvature flow starting at any sufficiently small perturbation of $M_0$ can also develop only neckpinch type singularities at the first singular time. We also show stability of nondegenerate neckpinch singularities in the above sense, which speaks in favor of stability of Type I singularities.
