Communications in Analysis and Geometry
Volume 24 (2016)
Holomorphic triples and the prescribed curvature problem on $S^2$
Pages: 559 – 591
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.
holomorphic triples, conformal curvature equations, cohomology classes
2010 Mathematics Subject Classification
32F32, 35J15, 58J05