Complete translating solitons to the mean curvature flow in ℝ3 with nonnegative mean curvature

By J. Spruck, Ling Xiao. American Journal of Mathematics, 2020

82 citations recorded by the source corpus.

abstract:We prove that any complete immersed two-sided mean convex translating soliton $\Sigma\subset{\Bbb R}^3$ for the mean curvature flow is convex. As a corollary it follows that an entire mean convex graphical translating soliton in ${\Bbb R}^3$ is the axisymmetric "bowl soliton". We also show that if the mean curvature of $\Sigma$ tends to zero at infinity, then $\Sigma$ 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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/05a1985dd35a5e3a4aa6834044e788d936345d73

Citations in the corpus

• Graphical translators for mean curvature flow (2018, unknown): “□ The following very useful gradient bound, which plays a crucial role in this paper, is also due to Spruck and Xiao [SX17]: Theorem 2.6.”