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arXiv · 1704.04823

Spherical metrics with conical singularities on 2-spheres

Subhadip Dey
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Abstract

Suppose that $\theta_1,\theta_2,\dots,\theta_n$ are positive numbers and $n\ge 3$. Does there exist a sphere with a spherical metric with $n$ conical singularities of angles $2\pi\theta_1,2\pi\theta_2,\dots,2\pi\theta_n$? A sufficient condition was obtained by Gabriele Mondello and Dmitri Panov (arXiv:1505.01994). We show that it is also necessary when we assume that $\theta_1,\theta_2,\dots,\theta_n \not\in \mathbb{N}$.

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Subhadip Dey. 2017-04-16. Spherical metrics with conical singularities on 2-spheres. https://doi.org/10.1007/s10711-017-0306-1

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