Institute for Mathematical Sciences

Preprint ims01-14

Jeremy Tyson
On the conformal dimensions of quasiconvex post-critically finite self similar sets

Abstract: The conformal dimension of a metric space is the infimum of the Hausdorff dimensions of all quasisymmetrically equivalent metrics on the space. We show that certain classical self-similar fractal subsets of Euclidean space are not minimal for conformal dimension by constructing explicit metrics in the quasisymmetry class of the Euclidean metric with reduced Hausdorff dimension.
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