Metrics of constant positive curvature with four conic singularities on the sphere

Eremenko, Alexandre

doi:10.1090/proc/15012

Metrics of constant positive curvature with four conic singularities on the sphere
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Proc. Amer. Math. Soc. 148 (2020), 3957-3965 Request permission

Abstract:

We show that for given four points on the sphere and prescribed angles at these points which are not multiples of $2\pi$, the number of metrics of curvature $1$ having conic singularities with these angles at these points is finite.

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