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Zh. Mat. Fiz. Anal. Geom., 2016, Volume 12, Number 2, Pages 134–167 (Mi jmag649)  

This article is cited in 2 scientific papers (total in 2 papers)

Spherical quadrilaterals with three non-integer angles

A. Eremenkoa, A. Gabrielova, V. Tarasovbc

a Department of Mathematics, Purdue University, West Lafayette, IN 47907-2067 USA
b St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 27 Fontanka, St. Petersburg, 191023, Russia
c Department of Mathematical Sciences, IUPUI, Indianapolis, IN 46202-3216 USA

Abstract: A spherical quadrilateral is a bordered surface homeomorphic to a closed disk, with four 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 quadrilaterals and perform the classification up to isometry in the case that one corner of a quadrilateral is integer (i.e., its angle is a multiple of $\pi$) while the angles at its other three corners are not multiples of $\pi$. The problem is equivalent to classification of Heun's equations with real parameters and unitary monodromy, with the trivial monodromy at one of its four singular point.

Key words and phrases: surfaces of positive curvature, conic singularities, Heun equation, Schwarz equation, accessory parameter, conformal mapping, circular polygon.

Funding Agency Grant Number
National Science Foundation DMS-1361836
DMS-116162
Supported by NSF grant DMS-1361836.
Supported by NSF grant DMS-1161629.


DOI: https://doi.org/10.15407/mag12.02.134

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Document Type: Article
MSC: 30C20,34M03
Received: 07.07.2015
Language: English

Citation: A. Eremenko, A. Gabrielov, V. Tarasov, “Spherical quadrilaterals with three non-integer angles”, Zh. Mat. Fiz. Anal. Geom., 12:2 (2016), 134–167

Citation in format AMSBIB
\Bibitem{EreGabTar16}
\by A.~Eremenko, A.~Gabrielov, V.~Tarasov
\paper Spherical quadrilaterals with three non-integer angles
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2016
\vol 12
\issue 2
\pages 134--167
\mathnet{http://mi.mathnet.ru/jmag649}
\crossref{https://doi.org/10.15407/mag12.02.134}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3498735}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000378645600003}
\elib{http://elibrary.ru/item.asp?id=25955929}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Eremenko, A. Gabrielov, “Circular pentagons and real solutions of Painlevé VI equations”, Commun. Math. Phys., 355:1 (2017), 51–95  crossref  mathscinet  zmath  isi  scopus
    2. Alexandre Eremenko, Vitaly Tarasov, “Fuchsian Equations with Three Non-Apparent Singularities”, SIGMA, 14 (2018), 058, 12 pp.  mathnet  crossref
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