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

作者：Zhang Tanran^*

来源：Bulletin of the Korean Mathematical Society, 2014, 51(5): 1485-1502.

DOI：10.4134/BKMS.2014.51.5.1485

• conical singularities
• hyperbolic metrics
• special functions

The explicit formula for the hyperbolic metric lambda(alpha,) (beta,) (gamma)(z)\dz\ on the thrice-punctured sphere P\{0, 1, infinity} with singularities of order 0 < alpha, beta < 1, gamma <= 1, alpha + beta + gamma > 2 at 0, 1, infinity was given by Kraus, Roth and Sugawa in [9]. In this article we investigate the asymptotic properties of the higher order derivatives of lambda(alpha,) (beta,) (gamma)(z) near the origin and give more precise descriptions for the asymptotic behavior of lambda(alpha,) (beta,) (gamma)(z).

• 出版日期2014-9