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

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

2009-03-10

arxiv.org/abs/0903.1761v2

Mathematics

Complex Variables

13 pages

Scientific paper

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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