Vol. 14, No. 3, 2021

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

Tobias Lamm, Andrea Malchiodi and Mario Micallef

Vol. 14 (2021), No. 3, 881–889

We consider approximations introduced by Sacks and Uhlenbeck of the harmonic energy for maps from S2 into S2. We continue our previous analysis (J. Differential Geom. 116:2 (2020), 321–348) on limits of α-harmonic maps with uniformly bounded energy. Using a recent energy identity of Li and Zhu (Ann. Inst. H. Poincaré Anal. Non Linéaire 36:1 (2019), 103–118), we obtain an optimal gap theorem for the α-harmonic maps of degree 1,0 or 1.

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$\alpha$-harmonic maps, gap theorems
Mathematical Subject Classification 2010
Primary: 58E20
Received: 25 March 2019
Accepted: 21 November 2019
Published: 18 May 2021
Tobias Lamm
Institute for Analysis
Karlsruhe Institute of Technology
Andrea Malchiodi
Scuola Normale Superiore
Mario Micallef
Mathematics Institute
University of Warwick
United Kingdom