Energy identity and no neck property for $\varepsilon$-harmonic and $\alpha$-harmonic maps into homogeneous target manifolds

TL;DR

This paper establishes energy identity and no-neck property for psilon- and lpha-harmonic maps into homogeneous manifolds, introducing an equivariant embedding technique for the psilon case.

Contribution

It proves the energy identity and no-neck property for these harmonic maps, with a novel approach using equivariant embeddings for psilon-harmonic maps.

Findings

Energy identity is confirmed for psilon- and lpha-harmonic maps.

No-neck property is established for these maps.

A new method using equivariant embedding is introduced for psilon-harmonic maps.

Abstract

In this paper we show the energy identity and the no-neck property for $\varepsilon$- and $\alpha$-harmonic maps with homogeneous target manifolds. To prove this in the $\varepsilon$-harmonic case we introduce the idea of using an equivariant embedding of the homogeneous target manifold.