Dimension distortion of hyperbolically convex maps
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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 $1.$References
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Additional Information
- S. Rohde
- Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1169-1173
- MSC (2000): Primary 30C35
- DOI: https://doi.org/10.1090/S0002-9939-06-08562-5
- MathSciNet review: 2262922