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 \({\mathbb {R}}^{n+1},\, n\ge 3 \) is the axisymmetric “bowl soliton.”
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Spruck, J., Sun, L. Convexity of 2-Convex Translating Solitons to the Mean Curvature Flow in \(\pmb {\varvec{{\mathbb {R}}}}^{n+1}\). J Geom Anal 31, 4074–4091 (2021). https://doi.org/10.1007/s12220-020-00427-w
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DOI: https://doi.org/10.1007/s12220-020-00427-w
Keywords
- Mean curvature flow
- Entire translating soliton
- Uniform 2-convexity
- Bowl soliton
- Convexity
- Fully nonlinear elliptic