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

: Anderson G, Sugawa T, Vamanamurthy M, Vuorinen M

: 2010

: Mathematische Zeitschrift

: 1

: 266

: 1

: 181

: 191

: 11

: 0025-5874

DOI: https://doi.org/10.1007/s00209-009-0560-5

: http://api.elsevier.com/content/abstract/scopus_id:77954538835

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. © Springer-Verlag 2009.