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arxiv: 0903.1761 · v2 · submitted 2009-03-10 · 🧮 math.CV · math.CA

Twice-punctured hyperbolic sphere with a conical singularity and generalized elliptic integral

classification 🧮 math.CV math.CA
keywords conicalellipticgeneralizedhyperbolicmetricsingularityspheretwice-punctured
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We describe, in terms of generalized elliptic integrals, the hyperbolic metric of the twice-punctured sphere with one conical singularity of prescribed order. We also give several monotonicity properties of the metric and a couple of applications.

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