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

Author:

José Torres Santaella

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Analysis of PDEs (math.AP)

journal:

date:

2023-06-05 16:00:00

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.

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