Invariant surfaces in Euclidean space with a log-linear density

Abstract

A λ-translating soliton with density vector v→ is a surface in Euclidean space whose mean curvature H satisfies 2H=2λ+〈N,v→〉, where N is the Gauss map. We classify all λ-translating solitons that are invariant by a one-parameter group of translations and a one-parameter group of rotations.