A gap theorem for $\alpha$-harmonic maps between two-spheres

Abstract

In this paper we consider approximations introduced by Sacks-Uhlenbeck of the harmonic energy for maps from $S^2$ into $S^2$. We continue the analysis in [6] about limits of $\alpha$-harmonic maps with uniformly bounded energy. Using a recent energy identity in [7], we obtain an optimal gap theorem for the $\alpha$-harmonic maps of degree $-1,0$ or $1$.

Statement of the old Theorem 1.2 and its proof have been corrected, to appear in Anal. PDE

References in corpus (1)

• A conformally invariant gap theorem in Yang-Mills theory

Cited by in corpus (1)

• Minimal $W^{s,\frac{n}{s}}$-harmonic maps in homotopy classes