A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Some inequalities for the Poincaré metric of plane domains
Tekijät: Sugawa T., Vuorinen M.
Julkaisuvuosi: 2005
Journal: Mathematische Zeitschrift
Tietokannassa oleva lehden nimi: Mathematische Zeitschrift
Vuosikerta: 250
Numero: 4
Aloitussivu: 885
Lopetussivu: 906
Sivujen määrä: 22
ISSN: 0025-5874
DOI: https://doi.org/10.1007/s00209-005-0782-0
Verkko-osoite: http://api.elsevier.com/content/abstract/scopus_id:23744456000
Tiivistelmä
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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