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

 

Dimension distortion of hyperbolically convex maps


Author: S. Rohde
Journal: Proc. Amer. Math. Soc. 135 (2007), 1169-1173
MSC (2000): Primary 30C35
Published electronically: November 13, 2006
MathSciNet review: 2262922
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Abstract: In this note, we provide an answer to a question of D. Mejia and Chr. Pommerenke, by constructing a hyperbolically convex subdomain $ G$ of the unit disc $ \mathbb{D}$ so that the conformal map from $ \mathbb{D}$ to $ G$ maps a set of dimension 0 on $ \partial\mathbb{D}$ to a set of dimension $ 1.$


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Additional Information

S. Rohde
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08562-5
PII: S 0002-9939(06)08562-5
Received by editor(s): November 9, 2004
Received by editor(s) in revised form: November 16, 2005
Published electronically: November 13, 2006
Additional Notes: The author was partially supported by NSF Grants DMS-0201435 and DMS-0244408.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.