# Energy identity and no neck property for ε-harmonic and α-harmonic maps into homogeneous target manifolds

## TL;DR

This paper proves energy identity and no-neck property for ε- and α-harmonic maps into homogeneous manifolds.

## Contribution

The novel approach involves using an equivariant embedding of the homogeneous target manifold.

## Key findings

- Energy identity is established for ε- and α-harmonic maps into homogeneous manifolds.
- The no-neck property is proven using an equivariant embedding technique.

## Abstract

In this paper we show the energy identity and the no-neck property for \documentclass[12pt]{minimal}
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\begin{document}$$\varepsilon $$\end{document}ε- and \documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}α-harmonic maps with homogeneous target manifolds. To prove this in the \documentclass[12pt]{minimal}
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\begin{document}$$\varepsilon $$\end{document}ε-harmonic case we introduce the idea of using an equivariant embedding of the homogeneous target manifold.