Harmonic maps of degree 1 into the unit 2-sphere (Q5929576)

Following the method used in [\textit{J.-M. Coron}, C. R. Acad. Sci., Paris, Sér. I 299, 209-212 (1984; Zbl 0569.35032) and \textit{Y. Ge}, ESAIM, Control Optim. Calc. Var. 3, 263-300 (1998; Zbl 0903.53003)], the main result here states that there exists an open subset \(H\) in the Teichmüller space of genus \(g\geq 2\) such that for each Riemann surface \(P\subset H\), there is a harmonic map of degree 1 from \(P\) to the unit sphere \(S^2\).