Some inequalities for the Poincaré metric of plane domains
Some inequalities for the Poincaré metric of plane domains
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DOI：
10.1007/s00209-005-0782-0
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发表时间：
2005-04
影响因子：
0.8
通讯作者：
T. Sugawa;M. Vuorinen
中科院分区：
文献类型：
--
作者：
T. Sugawa;M. Vuorinen
本文在平面区域的Poincaré（或双曲）度量及其距离的详细性质的基础上，研究了平面区域的Poincaré（或双曲）度量及其距离 特别地，给出了加德纳和Lakic [7]的一个结果的另一个证明.本文中的这个常数和其他一些常数涉及完全椭圆积分和相关特殊函数的特定值。给出了边界点附近双曲距离的具体估计，并由此导出了Littlewood定理的改进。
In this paper, the Poincaré (or hyperbolic) metric and the associated distance are investigated for a plane domain based on the detailed properties of those for the particular domain In particular, another proof of a recent result of Gardiner and Lakic [7] is given with explicit constant. This and some other constants in this paper involve particular values of complete elliptic integrals and related special functions. A concrete estimate for the hyperbolic distance near a boundary point is also given, from which refinements of Littlewood’s theorem are derived.