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Winter 2015 On metrics of curvature $1$ with four conic singularities on tori and on the sphere
Alexandre Eremenko, Andrei Gabrielov
Illinois J. Math. 59(4): 925-947 (Winter 2015). DOI: 10.1215/ijm/1488186015

Abstract

We discuss conformal metrics of curvature $1$ on tori and on the sphere, with four conic singularities whose angles are multiples of $\pi$. Besides some general results we study in detail the family of such symmetric metrics on the sphere, with angles $(\pi,3\pi,\pi,3\pi)$. As a consequence we find new Heun’s equations whose general solution is algebraic.

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Alexandre Eremenko. Andrei Gabrielov. "On metrics of curvature $1$ with four conic singularities on tori and on the sphere." Illinois J. Math. 59 (4) 925 - 947, Winter 2015. https://doi.org/10.1215/ijm/1488186015

Information

Received: 10 January 2016; Published: Winter 2015
First available in Project Euclid: 27 February 2017

zbMATH: 1366.30029
MathSciNet: MR3628295
Digital Object Identifier: 10.1215/ijm/1488186015

Subjects:
Primary: 30C20, 33E05, 34M03, 34M05, 35J91

Rights: Copyright © 2015 University of Illinois at Urbana-Champaign

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Vol.59 • No. 4 • Winter 2015
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