# On the stability of harmonic maps under the homogeneous Ricci flow

## TL;DR

This paper investigates how the stability of harmonic maps is affected by the homogeneous Ricci flow, providing examples of both preserved and non-preserved stability states.

## Contribution

It offers new insights into the stability behavior of harmonic maps under Ricci flow, including specific examples illustrating different stability outcomes.

## Key findings

- Stability can be preserved under Ricci flow in certain cases
- Non-stability of harmonic maps may not be preserved under Ricci flow
- Examples demonstrate both stability preservation and loss during Ricci flow

## Abstract

In this work we study properties of stability and non-stability of harmonic maps under the homogeneous Ricci flow. We provide examples where the stability (non-stability) is preserved under the Ricci flow and an example where the Ricci flow does not preserve the stability of an harmonic map.