Some inequalities for the Poincaré metric of plane domains | Zendy

Toshiyuki Sugawa | Zendy; Матти Вуоринен | Zendy

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Some inequalities for the Poincaré metric of plane domains

Author(s) -

Toshiyuki Sugawa,

Матти Вуоринен

Publication year - 2005

Publication title -

mathematische zeitschrift

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.38

H-Index - 66

eISSN - 1432-1823

pISSN - 0025-5874

DOI - 10.1007/s00209-005-0782-0

Subject(s) - mathematics , inequality , metric (unit) , pure mathematics , plane (geometry) , poincaré conjecture , algebra over a field , mathematical analysis , geometry , operations management , economics

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.

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