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Please use this identifier to cite or link to this item:
http://hdl.handle.net/10016/6505
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| Title: | Radial images by holomorphic mappings |
| Author(s): | Fernández, José L.
Pestana, Domingo |
| Publisher: | American Mathematical Society |
| Issued date: | Feb-1996 |
| Citation: | Proceedings of the American Mathematical Society, 1996, vol. 124, n. 2, p. 429-435 |
| URI: | http://hdl.handle.net/10016/6505 |
| ISSN: | 0002-9939 (Print)
1088-6826 (Online) |
| DOI: | 10.1090/S0002-9939-96-02971-1 |
| Description: | 7 pages, no figures.-- MSC1991 codes: Primary 30E25, 30F45.
MR#: MR1283549 (96d:30007)
Zbl#: Zbl 0845.30030 |
| 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. |
| Sponsor: | Research supported by a grant of CICYT, Ministerio de Educación y Ciencia, Spain. |
| Review: | PeerReviewed |
| Publisher version: | http://dx.doi.org/10.1090/S0002-9939-96-02971-1 |
| Keywords: | Exponent of convergence
Hausdorff dimension
Poincaré distance
Geodesic
Radial image |
| Rights: | © American Mathematical Society |
| Appears in Collections: | DM - GAMA - Artículos de Revistas
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