We show that the Bowl soliton in ${ℝ}^3$ is the unique translating solution of the mean curvature flow whose tangent flow at $-\infty$ is the shrinking cylinder. As an application, we show that for a generic mean curvature flow, all (non-static) translating limit flows are the bowl soliton. The crucial point is that we do not make any global convexity assumption, while as the same time, the asymptotic requirement is very weak.

中文翻译：

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渐近圆柱体的翻译器

我们证明了碗孤子 ${ℝ}^3$ 是平均曲率流的唯一平移解，其切线流在 $--\infty$是收缩筒。作为应用，我们表明对于一般的平均曲率流，所有（非静态）平移极限流都是碗孤子。关键点是，我们不做任何全局凸性假设，而同时，渐近性要求非常弱。