Conformal dimension of the antenna set
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- by Christopher J. Bishop and Jeremy T. Tyson PDF
- Proc. Amer. Math. Soc. 129 (2001), 3631-3636 Request permission
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
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Additional Information
- Christopher J. Bishop
- Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651
- MR Author ID: 37290
- Email: bishop@math.sunysb.edu
- Jeremy T. Tyson
- Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651
- MR Author ID: 625886
- Email: tyson@math.sunysb.edu
- 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
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1860497