Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Radial images by holomorphic mappings


Authors: José L. Fernández and Domingo Pestana
Journal: Proc. Amer. Math. Soc. 124 (1996), 429-435
MSC (1991): Primary 30E25, 30F45
MathSciNet review: 1283549
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30E25, 30F45

Retrieve articles in all journals with MSC (1991): 30E25, 30F45


Additional Information

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

Domingo Pestana
Affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Address at time of publication: Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganes, Spain
Email: dompes@arwen.uc3m.es

DOI: http://dx.doi.org/10.1090/S0002-9939-96-02971-1
PII: S 0002-9939(96)02971-1
Received by editor(s): May 6, 1994
Received by editor(s) in revised form: June 16, 1994
Additional Notes: Research supported by a grant of CICYT, Ministerio de Educación y Ciencia, Spain.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia