A Schwarz lemma for meromorphic functions and estimates for the hyperbolic metric
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- by Alexander Yu. Solynin PDF
- Proc. Amer. Math. Soc. 136 (2008), 3133-3143 Request permission
Abstract:
We prove a generalization of the Schwarz lemma for meromorphic functions $f$ mapping the unit disk $\mathbb {D}$ onto Riemann surfaces ${\mathcal {R}}$ with bounded in mean radial distances from $f(0)$ to the boundary of ${\mathcal {R}}$. A new variant of the Schwarz lemma is also proved for the Carathèodory class of analytic functions having positive real part in $\mathbb {D}$. Our results lead to several improved estimates for the hyperbolic metric.References
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Additional Information
- Alexander Yu. Solynin
- Affiliation: Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, Texas 79409
- MR Author ID: 206458
- Email: alex.solynin@ttu.edu
- Received by editor(s): April 30, 2007
- Published electronically: May 5, 2008
- Additional Notes: This research was supported in part by NSF grant DMS-0525339
- Communicated by: Ronald A. Fintushel
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3133-3143
- MSC (2000): Primary 30C80
- DOI: https://doi.org/10.1090/S0002-9939-08-09309-X
- MathSciNet review: 2407076