Asymptotic properties of the hyperbolic metric on the sphere with three conical singularities

Tanran Zhang

Asymptotic properties of the hyperbolic metric on the sphere with three conical singularities

Complex Variables 2013-01-31 v1

Authors: Tanran Zhang

Abstract

The explicit formula for the hyperbolic metric $\lambda_{\alpha,\,\beta,\,\gamma}(z)|dz|$ on the thrice-punctured sphere $\mathbb{P} \backslash \{z_1,\,z_2,\,z_3\}$ with singularities of order $\alpha,\,\beta,\,\gamma \leq 1$ with $\alpha+\beta+\gamma>2$ at $z_1,\,z_2,\,z_3$ was given by Kraus, Roth and Sugawa in \cite{Rothhyper}. In this paper we investigate the asymptotic properties of the higher order derivatives of $\lambda_{\alpha,\,\beta,\,\gamma}(z)$ near the singularity and give some more precise description for the asymptotic behavior.

Keywords

hyperbolic metric conical singularities thrice-punctured sphere asymptotic properties higher order derivatives complex analysis

Cite

@article{arxiv.1301.7272,
  title  = {Asymptotic properties of the hyperbolic metric on the sphere with three conical singularities},
  author = {Tanran Zhang},
  journal= {arXiv preprint arXiv:1301.7272},
  year   = {2013}
}

Asymptotic properties of the hyperbolic metric on the sphere with three conical singularities

Abstract

Keywords

Cite

Related papers