Asymptotic properties of the hyperbolic metric on the sphere with three conical singularities
Abstract
The explicit formula for the hyperbolic metric λα,\,β,\,γ(z)|dz| on the thrice-punctured sphere P \z1,\,z2,\,z3\ with singularities of order α,\,β,\,γ ≤ 1 with α+β+γ>2 at z1,\,z2,\,z3 was given by Kraus, Roth and Sugawa in Rothhyper. In this paper we investigate the asymptotic properties of the higher order derivatives of λα,\,β,\,γ(z) near the singularity and give some more precise description for the asymptotic behavior.
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