For every s in (0,1), infinitely many Hopf homotopy classes of pi_3(S^2) contain a minimizing W^{s,3/s}-harmonic map.
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Existence of infinitely many homotopy classes from $\mathbb S^3$ to $\mathbb S^2$ having a minimimzing $W^{s,\frac 3s}$-harmonic map
For every s in (0,1), infinitely many Hopf homotopy classes of pi_3(S^2) contain a minimizing W^{s,3/s}-harmonic map.