ASYMPTOTIC PROPERTIES OF THE HYPERBOLIC METRIC ON THE SPHERE WITH THREE CONICAL SINGULARITIES

Title & Authors
ASYMPTOTIC PROPERTIES OF THE HYPERBOLIC METRIC ON THE SPHERE WITH THREE CONICAL SINGULARITIES
Zhang, Tanran;

Abstract
The explicit formula for the hyperbolic metric $\small{{\lambda}_{{\alpha},{\beta},{\gamma}}(z){\mid}dz{\mid}}$ on the thrice-punctured sphere $\small{\mathbb{P}{\backslash}\{0,1,{\infty}\}}$ with singularities of order 0 < $\small{{\alpha}}$, $\small{{\beta}}$ < 1, $\small{{\gamma}{\leq}1}$, $\small{{\alpha}+{\beta}+{\gamma}}$ > 2 at 0, 1, $\small{{\infty}}$ was given by Kraus, Roth and Sugawa in [9]. In this article we investigate the asymptotic properties of the higher order derivatives of $\small{{\lambda}_{{\alpha},{\beta},{\gamma}}(z)}$ near the origin and give more precise descriptions for the asymptotic behavior of $\small{{\lambda}_{{\alpha},{\beta},{\gamma}}(z)}$.
Keywords
conical singularities;hyperbolic metrics;special functions;
Language
English
Cited by
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