Calculus of Variations and Geometric Measure Theory

T. Lamm - A. Malchiodi - M. Micallef

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

created by malchiodi on 09 Apr 2019
modified on 07 Dec 2020


Submitted Paper

Inserted: 9 apr 2019
Last Updated: 7 dec 2020

Pages: 9
Year: 2019


In this paper we consider approximations à la 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 $1$.