Ruled surfaces as translating solitons of the inverse mean curvature flow in the three-dimensional Lorentz-Minkowski space

Abstract

In this paper, we classify the nondegenerate ruled surfaces in the three-dimensional Lorentz-Minkowski space that are translating solitons for the inverse mean curvature flow. In particular, we prove the existence of non-cylindrical ruled translating solitons, which contrast with the Euclidean setting.