Conformal dimension of the antenna set

Christopher Bishop, Jeremy Tyson

Source record

Source: Crossref

Published: Apr 25, 2001

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

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Source abstract

We show that the self-similar set known as the “antenna set” has the property that inf f dim ⁡ ( f ( X ) ) = 1 \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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