Self similar solutions to the inverse mean curvature flow in $\mathbb{R}^2$

TL;DR

This paper classifies all self-similar solutions to the inverse mean curvature flow in the plane, providing a comprehensive understanding of their structure and properties.

Contribution

It offers a complete list of self-similar solutions to the inverse mean curvature flow in two-dimensional Euclidean space, filling a gap in the mathematical literature.

Findings

Complete classification of self-similar solutions

Identification of explicit solution forms

Insights into geometric properties of solutions

Abstract

In this paper, we obtain a complete list of all self-similar solutions of inverse mean curvature flow in $\mathbb{R}^2$.