Maximum Principles and Consequences for $\gamma$-translators in ${\mathbb{R}}^{n+1}$

Abstract

In this paper we obtain several properties of translating solitons for a general class of extrinsic geometric curvature flows given by a homogeneous, symmetric, smooth non-negative function $\gamma$ defined in an open cone $\Gamma \subset {\mathbb{R}}^n$. The main results are tangential principles, nonexistence theorems for closed and entire solutions, and a uniqueness result that says that any strictly convex $\gamma$-translator defined on a ball with a single end ${\mathcal{C}}^2$-asymptotic to a cylinder is the ''bowl''-type solution found in the translator paper of S. Rengaswami.

Comments are welcome!

References in corpus (1)

• Translating Solutions of a Generalized Mean Curvature Flow in a Cylinder: I. Constant Boundary Angles