We prove that any complete immersed two-sided mean convex translating soliton Σ ⊂ R for the mean curvature flow is convex. As a corollary it follows that an entire mean convex graphical translating soliton in R is the axisymmetric “bowl soliton”. We also show that if the mean curvature of Σ tends to zero at infinity, then Σ can be represented as an entire graph and so is the “bowl soliton”. Finally we classify the asymptotic behavior of all locally strictly convex graphical translating solitons defined over strip regions.

中文翻译：

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将孤子完全转换为 ℝ3 中的平均曲率流，平均曲率非负

我们证明了平均曲率流的任何完全浸入式两侧平均凸平移孤子 Σ ⊂ R 都是凸的。作为推论，R 中的整个平均凸图形平移孤子是轴对称的“碗孤子”。我们还表明，如果 Σ 的平均曲率在无穷远处趋于零，那么 Σ 可以表示为一个完整的图，“碗孤子”也是如此。最后，我们对在条带区域上定义的所有局部严格凸图形平移孤子的渐近行为进行分类。