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

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.