Selfsimilar expanders of the harmonic map flow

TL;DR

This paper investigates the existence, uniqueness, and stability of self-similar solutions to the harmonic map heat flow, emphasizing the role of energy-minimizing equator maps in these properties.

Contribution

It establishes the existence of self-similar expanders for any admissible initial data and links their uniqueness and stability to energy-minimizing equator maps.

Findings

Existence of self-similar solutions for all admissible initial data.

Uniqueness and stability are governed by energy-minimizing properties.

Self-similar expanders are characterized in equivariant settings.

Abstract

We study the existence, uniqueness, and stability of self-similar expanders of the harmonic map heat flow in equivariant settings. We show that there exist selfsimilar solutions to any admissiable initial data and that their uniqueness and stability properties are essentially determined by the energy-minimising properties of the so called equator maps.