We consider a nondegenerate case of generic singularity when the limit cylinder of the rescaled mean curvature flow is \({\mathbb {R}}^3 \times {\mathbb {S}}^1\). We obtain a detailed description of a possibly small, but fixed, neighborhood of the singularity, up to (and including) the blowup time, and find that it is mean convex and the singularity is isolated. In the considered nondegenerate cases, we confirm the conjectures of mean convexity and isolation of singularities.

中文翻译：

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由平均曲率流形成的一般奇点的时空邻域的平均凸性

当重新定标的平均曲率流的极限圆柱为\（{\ mathbb {R}} ^ 3 \ times {\ mathbb {S}} ^ 1 \）时，我们考虑泛型奇点的非退化情况。我们获得了一个可能很小但固定的奇点附近的详细描述，直到（包括）爆破时间为止，并且发现它是平均凸点，并且奇点是孤立的。在考虑的非退化情况下，我们证实了平均凸度和奇异性隔离的猜想。