Metrics with four conic singularities and spherical quadrilaterals
Complex Variables
2016-09-27 v1 Classical Analysis and ODEs
Metric Geometry
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 two angles at the corners are multiples of pi. The problem is equivalent to classification of Heun's equations with real parameters and unitary monodromy.
Keywords
Cite
@article{arxiv.1409.1529,
title = {Metrics with four conic singularities and spherical quadrilaterals},
author = {Alexandre Eremenko and Andrei Gabrielov and Vitaly Tarasov},
journal= {arXiv preprint arXiv:1409.1529},
year = {2016}
}
Comments
68 pges, 25 figures