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## Spherical metrics with conical singularities on 2-spheres

- Author(s): Dey, Subhadip;
- et al.

## Published Web Location

https://arxiv.org/pdf/1704.04823.pdfNo data is associated with this publication.

## Abstract

Suppose that θ1,θ2,…,θn are positive numbers and n≥3. Does there exist a sphere with a spherical metric with n conical singularities of angles 2πθ1,2πθ2,…,2πθn? A sufficient condition was obtained by Gabriele Mondello and Dmitri Panov (arXiv:1505.01994 https://arxiv.org/abs/1505.01994). We show that it is also necessary when we assume that θ1,θ2,…,θn∉N.