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arXiv · 1910.02195

Convexity of 2-convex translating solitons to the mean curvature flow in $\mathbb{R}^{n+1}$

Joel Spruck·Liming Sun
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Abstract

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\geq 3 $ is the axisymmetric "bowl soliton".

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Joel Spruck, Liming Sun. 2019-10-05. Convexity of 2-convex translating solitons to the mean curvature flow in $\mathbb{R}^{n+1}$. https://doi.org/10.1007/s12220-020-00427-w

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