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Conformal dimension of the antenna set |
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| Authors: | Christopher J. Bishop Jeremy T. Tyson |
| Affiliation: | Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651 ; Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651 |
| Abstract: | We show that the self-similar set known as the ``antenna set' has the property that |
| Keywords: | Quasiconformal map Hausdorff dimension conformal dimension self-similar sets |
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(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.