A Schwarz lemma for meromorphic functions and estimates for the hyperbolic metric

Author:
Alexander Yu. Solynin

Journal:
Proc. Amer. Math. Soc. **136** (2008), 3133-3143

MSC (2000):
Primary 30C80

DOI:
https://doi.org/10.1090/S0002-9939-08-09309-X

Published electronically:
May 5, 2008

MathSciNet review:
2407076

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Abstract: We prove a generalization of the Schwarz lemma for meromorphic functions mapping the unit disk onto Riemann surfaces with bounded in mean radial distances from to the boundary of . A new variant of the Schwarz lemma is also proved for the Carathèodory class of analytic functions having positive real part in . Our results lead to several improved estimates for the hyperbolic metric.

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Additional Information

**Alexander Yu. Solynin**

Affiliation:
Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, Texas 79409

Email:
alex.solynin@ttu.edu

DOI:
https://doi.org/10.1090/S0002-9939-08-09309-X

Keywords:
Schwarz lemma,
meromorphic function,
hyperbolic metric,
reduced module,
polarization

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

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.