A1 Refereed original research article in a scientific journal
Some inequalities for the Poincaré metric of plane domains
Authors: Sugawa T., Vuorinen M.
Publication year: 2005
Journal:: Mathematische Zeitschrift
Journal name in source: Mathematische Zeitschrift
Volume: 250
Issue: 4
First page : 885
Last page: 906
Number of pages: 22
ISSN: 0025-5874
DOI: https://doi.org/10.1007/s00209-005-0782-0
Web address : http://api.elsevier.com/content/abstract/scopus_id:23744456000
Abstract
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 [InlineMediaObject not available: see fulltext.] In particular another proof of a recent result of Gardiner and Lakic 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. © Springer-Verlag Berlin Heidelberg 2005.
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 [InlineMediaObject not available: see fulltext.] In particular another proof of a recent result of Gardiner and Lakic 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. © Springer-Verlag Berlin Heidelberg 2005.
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