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
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.
|National Science Foundation
|Supported by NSF grant DMS-1361836.
Supported by NSF grant DMS-1161629.
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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
\by A.~Eremenko, A.~Gabrielov, V.~Tarasov
\paper Spherical quadrilaterals with three non-integer angles
\jour Zh. Mat. Fiz. Anal. Geom.
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This publication is cited in the following articles:
A. Eremenko, A. Gabrielov, “Circular pentagons and real solutions of Painlevé VI equations”, Commun. Math. Phys., 355:1 (2017), 51–95
Alexandre Eremenko, Vitaly Tarasov, “Fuchsian Equations with Three Non-Apparent Singularities”, SIGMA, 14 (2018), 058, 12 pp.
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