Proceedings of the American Mathematical Society

Author(s): Christopher J. Bishop; Jeremy T. Tyson
Journal: Proc. Amer. Math. Soc. 129 (2001), 3631-3636.
MSC (2000): Primary 30C62; Secondary 28A78
Posted: April 25, 2001
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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.

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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: 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
Posted: 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
Copyright of article: Copyright 2001, American Mathematical Society

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