We prove that any complete immersed globally orientable uniformly 2-convex translating soliton \(\Sigma \subset {\mathbb {R}}^{n+1}\) for the mean curvature flow is locally strictly convex. It follows that a uniformly 2-convex entire graphical translating soliton in \({\mathbb {R}}^{n+1},\, n\ge 3 \) is the axisymmetric “bowl soliton.”

中文翻译：

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2-凸平移孤子到$$ \ pmb {\ varvec {{\ mathbb {R}}}} ^ {n + 1} $$ Rn + 1的平均曲率流的凸性

我们证明，平均曲率流的任何完全浸没的全局可定向的均匀2凸平移孤子\（\ Sigma \ subset {\ mathbb {R}} ^ {n + 1} \）都是局部严格凸的。因此，\（{{mathbb {R}} ^ {n + 1}，\，n \ ge 3 \）中均匀一致的2-凸整个图形平移孤子是轴对称的“碗孤子”。