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

TL;DR

This paper classifies nondegenerate ruled surfaces in 3D Lorentz-Minkowski space that serve as translating solitons for the inverse mean curvature flow, revealing unique non-cylindrical solutions not present in Euclidean space.

Contribution

It provides a classification of ruled surfaces as translating solitons in Lorentz-Minkowski space, including the existence of non-cylindrical solutions.

Findings

Existence of non-cylindrical ruled translating solitons.

Complete classification of such surfaces in Lorentz-Minkowski space.

Contrast with Euclidean case showing new solutions.

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.