Rotationally symmetric translating solitons of fully nonlinear extrinsic geometric flows: Classification and Applications

TL;DR

This paper classifies and analyzes rotationally symmetric translating solitons for fully nonlinear extrinsic geometric flows, providing asymptotic descriptions, uniqueness, and rigidity results under natural assumptions.

Contribution

It introduces a comprehensive classification of bowl and catenoidal-type solutions for these flows, including their asymptotic behaviors and uniqueness properties.

Findings

Established asymptotics of bowl-type evolutions

Constructed and classified catenoidal-type solutions

Proved rigidity and uniqueness under convexity assumptions

Abstract

We study rotationally symmetric translators for fully nonlinear extrinsic geometric flows driven by a curvature function, and we establish the fine asymptotics of bowl-type evolutions and, when admissible, the construction and classification of catenoidal-type solutions, together with their asymptotic behavior. Under natural structural and convexity assumptions, we also prove rigidity and uniqueness results within appropriate classes of graphical translators of such curvature flows.