arXiv subjects
Publications and source records attributed to Andrew M. Roberts.
In this paper we classify the low energy $\varepsilon$-harmonic maps from the surfaces of constant curvature with positive genus into the round sphere. We find that all such maps with degree $\pm1$ are all quantitively close to a bubble configuration with bubbles forming at special points on the domain with bubbling radius proportional to $\varepsilon^{1/4}$.
In this paper we find analogues for $\varepsilon$-harmonic maps to the generalised energy identity and the existence of geodesic necks result discovered by Yuxiang Li and Youde Wang for $\alpha$-harmonic maps. In particular there exist specific quantities depending only on $\varepsilon$ and the bubbling radius which entirely determine if the full energy identity holds and if a neck forms. In the case these fail we can calculate the energy lost and the length of the geodesic neck based on only these quantities and the biharmonic energy of the bubble.
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.