Classification of ruled surfaces as homothetic self-similar solutions of the inverse mean curvature flow in the Lorentz-Minkowski 3-space

TL;DR

This paper classifies certain ruled surfaces in Lorentz-Minkowski space that serve as self-similar solutions to the inverse mean curvature flow, revealing two distinct classes based on rulings.

Contribution

It provides a complete classification of nondegenerate ruled surfaces as homothetic self-similar solutions in Lorentz-Minkowski space, identifying two main classes.

Findings

Existence of two classes of homothetic solitons: lightlike and non-lightlike rulings.

Classification of nondegenerate ruled surfaces as solutions to the inverse mean curvature flow.

Insight into the geometric structure of self-similar solutions in Lorentz-Minkowski space.

Abstract

In this paper, we classify the nondegenerate ruled surfaces in the three-dimensional Lorentz-Minkowski space that are homothetic self-similar solutions for the inverse mean curvature flow. This classification shows the existence of two classes of non-cylindrical homothetic solitons: one with lightlike rulings and another one with non-lightlike rulings.