Abstract
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.
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D. Kraus was supported by a HWP scholarship
O. Roth and S. Ruscheweyh received partial support form the German-Israeli Foundation (grant G-809-234.6/2003)
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Kraus, D., Roth, O. & Ruscheweyh, S. A boundary version of Ahlfors’ Lemma, locally complete conformal metrics and conformally invariant reflection principles for analytic maps. J Anal Math 101, 219–256 (2007). https://doi.org/10.1007/s11854-007-0009-x
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DOI: https://doi.org/10.1007/s11854-007-0009-x