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

Alexandre C. Gonçalves

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arXiv · 1503.05886

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

Alexandre C. Gonçalves

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Abstract

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 2nd order on the sphere.

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BibTeX RIS

Alexandre C. Gonçalves. 2015-03-19. Holomorphic triples and the prescribed curvature problem on $S^2$. https://arxiv.org/abs/1503.05886

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