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arXiv · 1903.10217

A gap theorem for $α$-harmonic maps between two-spheres

Tobias Lamm·Andrea Malchiodi·Mario Micallef
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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 $α$-harmonic maps with uniformly bounded energy. Using a recent energy identity in [7], we obtain an optimal gap theorem for the $α$-harmonic maps of degree $-1, 0$ or $1$.

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Tobias Lamm, Andrea Malchiodi, Mario Micallef. 2020-12-07. A gap theorem for $α$-harmonic maps between two-spheres. https://doi.org/10.2140/apde.2021.14.881

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