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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A sharp Schwarz inequality on the boundary


Author: Robert Osserman
Journal: Proc. Amer. Math. Soc. 128 (2000), 3513-3517
MSC (2000): Primary 30C80
Published electronically: May 18, 2000
MathSciNet review: 1691000
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Abstract:

A number of classical results reflect the fact that if a holomorphic function maps the unit disk into itself, taking the origin into the origin, and if some boundary point $b$ maps to the boundary, then the map is a magnification at $b$. We prove a sharp quantitative version of this result which also sharpens a classical result of Loewner.


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Additional Information

Robert Osserman
Affiliation: MSRI, 1000 Centennial Drive, Berkeley, California 94720-5070
Email: osserman@msri.org

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05463-0
PII: S 0002-9939(00)05463-0
Keywords: Schwarz Lemma
Received by editor(s): June 15, 1998
Received by editor(s) in revised form: January 26, 1999
Published electronically: May 18, 2000
Additional Notes: The author’s research at MSRI is supported in part by NSF grant DMS-9701755.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society