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

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