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Fall 2014 Metrics with conic singularities and spherical polygons
Alexandre Eremenko, Andrei Gabrielov, Vitaly Tarasov
Illinois J. Math. 58(3): 739-755 (Fall 2014). DOI: 10.1215/ijm/1441790388


A spherical $n$-gon is a bordered surface homeomorphic to a closed disk, with $n$ distinguished boundary points called corners, equipped with a Riemannian metric of constant curvature $1$, except at the corners, and such that the boundary arcs between the corners are geodesic. We discuss the problem of classification of these polygons and enumerate them in the case that two angles at the corners are not multiples of $\pi$. The problem is equivalent to classification of some second order linear differential equations with regular singularities, with real parameters and unitary monodromy.


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Alexandre Eremenko. Andrei Gabrielov. Vitaly Tarasov. "Metrics with conic singularities and spherical polygons." Illinois J. Math. 58 (3) 739 - 755, Fall 2014.


Received: 8 May 2014; Revised: 31 March 2015; Published: Fall 2014
First available in Project Euclid: 9 September 2015

zbMATH: 06499620
MathSciNet: MR3395961
Digital Object Identifier: 10.1215/ijm/1441790388

Primary: 30C20, 34M03

Rights: Copyright © 2014 University of Illinois at Urbana-Champaign


Vol.58 • No. 3 • Fall 2014
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