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

 

Conformal dimension of the antenna set


Authors: Christopher J. Bishop and Jeremy T. Tyson
Journal: Proc. Amer. Math. Soc. 129 (2001), 3631-3636
MSC (2000): Primary 30C62; Secondary 28A78
Published electronically: April 25, 2001
MathSciNet review: 1860497
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Abstract | References | Similar Articles | Additional Information

Abstract:

We show that the self-similar set known as the ``antenna set'' has the property that $\inf_f \dim(f(X)) =1$ (where the infimum is over all quasiconformal mappings of the plane), but that this infimum is not attained by any quasiconformal map; indeed, is not attained for any quasisymmetric map into any metric space.


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

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Additional Information

Christopher J. Bishop
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651
Email: bishop@math.sunysb.edu

Jeremy T. Tyson
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651
Email: tyson@math.sunysb.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05982-2
PII: S 0002-9939(01)05982-2
Keywords: Quasiconformal map, Hausdorff dimension, conformal dimension, self-similar sets
Received by editor(s): November 15, 1999
Received by editor(s) in revised form: April 27, 2000
Published electronically: April 25, 2001
Additional Notes: The first author was partially supported by NSF Grant DMS 98-00924. The second author was partially supported by an NSF postdoctoral fellowship
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2001 American Mathematical Society