Conformal dimension of the antenna set

Christopher J. Bishop; Jeremy T. Tyson

doi:10.1090/s0002-9939-01-05982-2

Conformal dimension of the antenna set

Christopher J. Bishop, Jeremy T. Tyson

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the self-similar set known as the "antenna set" has the property that infy d\m(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.

Original language	English (US)
Pages (from-to)	3631-3636
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	129
Issue number	12
DOIs	https://doi.org/10.1090/s0002-9939-01-05982-2
State	Published - 2001
Externally published	Yes

Keywords

Conformai dimension
Hausdorff dimension
Quasiconformal map
Selfsimilar sets

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Online availability

10.1090/s0002-9939-01-05982-2

Library availability

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AB - We show that the self-similar set known as the "antenna set" has the property that infy d\m(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.

KW - Conformai dimension

KW - Hausdorff dimension

KW - Quasiconformal map

KW - Selfsimilar sets

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Conformal dimension of the antenna set

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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