A boundary version of Ahlfors’ Lemma, locally complete conformal metrics and conformally invariant reflection principles for analytic maps

A boundary version of Ahlfors’ Lemma, locally complete conformal metrics and conformally invariant reflection principles for analytic maps

A boundary version of Ahlfors' Lemma is established and used to show that the classical Schwarz-Carathéodory reflection principle for holomorphic functions has a purely conformal geometric formulation in terms of Riemannian metrics. This conformally invariant reflection principle generalizes na...

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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) Vol. 101; no. 1; pp. 219 - 256
Main Authors: Kraus, Daniela, Roth, Oliver, Ruscheweyh, Stephan
Format: Journal Article
Language:English
Published: Jerusalem Springer Nature B.V 01-03-2007
Subjects:
Principles
Online Access:Get full text
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Summary:A boundary version of Ahlfors' Lemma is established and used to show that the classical Schwarz-Carathéodory reflection principle for holomorphic functions has a purely conformal geometric formulation in terms of Riemannian metrics. This conformally invariant reflection principle generalizes naturally to analytic maps between Riemann surfaces and contains among other results a characterization of finite Blaschke products due to M. Heins.[PUBLICATION ABSTRACT]
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-007-0009-x