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

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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Bibliographic Details
Published in:Mathematische Zeitschrift 2010-09, Vol.266 (1), p.181-191
Main Authors: Anderson, G. D., Sugawa, T., Vamanamurthy, M. K., Vuorinen, M.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Description
Summary: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.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-009-0560-5