Asymptotic properties of the hyperbolic metric on the sphere with three conical singularities
Asymptotic properties of the hyperbolic metric on the sphere with three conical singularities
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DOI：
10.4134/bkms.2014.51.5.1485
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发表时间：
2013-01
期刊：
影响因子：
--
通讯作者：
Tanran Zhang
中科院分区：
文献类型：
--
作者：
Tanran Zhang
双曲度量$\lambda_{\alpha，\，\beta，\，\gamma}（z）的显式公式|DZ| Kraus，Roth和Sugawa在\cite{Rothhyper}中给出了三次穿孔球$\mathbb{P} \backslash \{z_1，\，z_2，\，z_3\}$上的奇异性为$\alpha，\，\beta，\，\gamma \leq 1$且$\alpha+\beta+\gamma>2$。本文研究了$\lambda_{\alpha，\，\beta，\，\gamma}（z）$的高阶导数在奇点附近的渐近性质，并给出了其渐近性态的更精确的描述.
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.