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

DOI:
https://doi.org/10.1090/S0002-9939-01-05982-2

Published electronically:
April 25, 2001

MathSciNet review:
1860497

Full-text PDF

Abstract | References | Similar Articles | Additional Information

We show that the self-similar set known as the ``antenna set'' has the property that (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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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:
https://doi.org/10.1090/S0002-9939-01-05982-2

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