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Constructive Methods of the Theory of Riemann Surfaces and Applications
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Flat cone metric space in terms of Schwarz-Christoffel maps S. Tanabéab a Galatasaray University, Istanbul b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region |
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Abstract: In this talk, we propose a complex analytic approach to the description of moduli space of flat metrics on a sphere with cone singularities. Namely, we consider the Schwarz-Christoffel map that sends a punctured upper half plane to a curvilinear polygon that shall be glued to form a surface with cone singularities. We discuss the relation with the monodromy invariant Hermitian form for Lauricella hypergeometric functions and the cone metric space as a hyperbolic space. Language: English |
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