Proceedings of the American Mathematical Society

Author(s): José L. Fernández; Domingo Pestana
Journal: Proc. Amer. Math. Soc. 124 (1996), 429-435.
MSC (1991): Primary 30E25, 30F45
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Abstract: Let $\mathcal{R}$ be a nonexceptional Riemann surface, other than the punctured disk. We prove that if $f$

is a holomorphic mapping from the unit disk $\Delta$ of the complex plane into $\mathcal{R}$ , then the set of radial images that remain bounded in the Poincaré metric of $\mathcal{R}$ has Hausdorff dimension at least $\delta (\mathcal{R})$ , the exponent of convergence of $\mathcal{R}$ . 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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30E25, 30F45

José L. Fernández
Affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Email: pando@ccuam3.sdi.uam.es

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