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Radial images by holomorphic mappings

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URI: https://hdl.handle.net/10016/6505
ISSN: 0002-9939 (Print)
ISSN: 1088-6826 (Online)
DOI: 10.1090/S0002-9939-96-02971-1
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radial_pestana_pams_1996.pdf (251.8 KB)
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1996-02
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American Mathematical Society
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Abstract
Let R be a nonexceptional Riemann surface, other than the punctured disk. We prove that if f is a holomorphic mapping from the unit disk Δ of the complex plane into R, then the set of radial images that remain bounded in the Poincaré metric of R has Hausdorff dimension at least δ(R), the exponent of convergence of R. The result is best possible. This is a hyperbolic analog of the result of N. G. Makarov that Bloch functions are bounded on a set of radii of dimension one.
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7 pages, no figures.-- MSC1991 codes: Primary 30E25, 30F45.
MR#: MR1283549 (96d:30007)
Zbl#: Zbl 0845.30030
Keywords
Exponent of convergence, Hausdorff dimension, Poincaré distance, Geodesic, Radial image
Bibliographic citation
Proceedings of the American Mathematical Society, 1996, vol. 124, n. 2, p. 429-435
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