Convexity estimate for translating solitons of concave fully nonlinear extrinsic geometric flows in $\mathbb{R}^{n+1}$

TL;DR

This paper establishes a convexity estimate for translating solitons in certain geometric flows, providing new insights into their structure and examples in Euclidean space.

Contribution

It introduces a convexity estimate for translating solitons under 1-homogeneous concave curvature functions, expanding understanding of their geometric properties.

Findings

Convexity estimate for solitons in extrinsic flows.

Examples of hypersurfaces in Euclidean space.

Insights into curvature-driven geometric evolution.

Abstract

The main result of this paper is a convexity estimate for translating solitons of extrinsic geometric flows which evolve under a $1$-homogeneous concave function in the principal curvatures. In addition, we show examples of these hypersurfaces in $\mathbb{R}^{n+1}$ for particular functions.