Communications in Analysis and Geometry

Volume 24 (2016)

Number 3

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

Pages: 559 – 591



Alexandre C. Gonçalves (Departamento de Computação e Matemática, Ribeirão Preto, SP, Brasil)


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

Published 22 June 2016