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arXiv · 2306.03649

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

José Torres Santaella
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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 $γ$ defined in an open cone $Γ\subset\mathbb{R}^n$. The main results are tangential principles, nonexistence theorems for closed and entire solutions, and a uniqueness result that says that any strictly convex $γ$-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.

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José Torres Santaella. 2023-06-06. Maximum Principles and Consequences for $γ$-translators in $\mathbb{R}^{n+1}$. https://doi.org/10.1112/blms.13004

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