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

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.