Some inequalities for the Poincaré metric of plane domains
Mathematische Zeitschrift Volume 250 Issue 4
Page 885-906
published_at 2005-08
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| File | |
| Title ( eng ) |
Some inequalities for the Poincaré metric of plane domains
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| Creator |
Sugawa Toshiyuki
Vuorinen Matti
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| Source Title |
Mathematische Zeitschrift
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| Volume | 250 |
| Issue | 4 |
| Start Page | 885 |
| End Page | 906 |
| 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 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.
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| NDC |
Mathematics [ 410 ]
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| Language |
eng
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| Resource Type | journal article |
| Publisher |
Springer
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| Date of Issued | 2005-08 |
| Rights |
Copyright (c) 2005 Springer-Verlag "The original publication is available at www.springer.com
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| Publish Type | Author’s Original |
| Access Rights | open access |
| Source Identifier |
[NCID] AA0072420X
[ISSN] 0025-5874
[DOI] 10.1007/s00209-005-0782-0
[DOI] http://dx.doi.org/10.1007/s00209-005-0782-0
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