Conformal Dimension of the Antenna Set

Abstract

We show that the self-similar set known as the “antenna set” has the property that inff 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. Given a compact metric space X we define its… (More)

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