Holomorphic triples and the prescribed curvature problem on $S^2$

We prove new results on existence of solutions for the prescribed gaussian curvature problem on the euclidean sphere $S^2$. Those results are achieved by relating this problem with the holomorphic triples theory on Riemann surfaces. We think this approach might be applied to study some other semi-linear elliptic equations of second order on the sphere.

Keywords

holomorphic triples, conformal curvature equations, cohomology classes

2010 Mathematics Subject Classification

32F32, 35J15, 58J05

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Published 22 June 2016