Low energy $\epsilon$-harmonic maps into the round sphere

In this paper we classify the low energy $\epsilon$-harmonic maps from the surfaces of constant curvature with positive genus into the round sphere. We find that all such maps with degree $\pm 1$ are all quantitively close to a bubble configuration with bubbles forming at special points on the domain with bubbling radius proportional to ${\epsilon }^{1\mathrm{/}4}$.