A sharp Schwarz inequality on the boundary
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- by Robert Osserman PDF
- Proc. Amer. Math. Soc. 128 (2000), 3513-3517 Request permission
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.References
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Additional Information
- Robert Osserman
- Affiliation: MSRI, 1000 Centennial Drive, Berkeley, California 94720-5070
- Email: osserman@msri.org
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3513-3517
- MSC (2000): Primary 30C80
- DOI: https://doi.org/10.1090/S0002-9939-00-05463-0
- MathSciNet review: 1691000