Dimension of quasicircles
We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala’s conjecture that the Hausdorff dimension of a k -quasicircle is at most 1+ k 2 .
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| Veröffentlicht in: | Acta mathematica 2010-09, Vol.205 (1), p.189-197 |
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| container_end_page | 197 |
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| container_title | Acta mathematica |
| container_volume | 205 |
| creator | Smirnov, Stanislav |
| description | We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala’s conjecture that the Hausdorff dimension of a
k
-quasicircle is at most 1+
k
2
. |
| doi_str_mv | 10.1007/s11511-010-0053-8 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 0001-5962 |
| ispartof | Acta mathematica, 2010-09, Vol.205 (1), p.189-197 |
| issn | 0001-5962 1871-2509 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_861544758 |
| source | International Press Journals; Project Euclid Open Access; EZB-FREE-00999 freely available EZB journals; SpringerLink Journals - AutoHoldings |
| subjects | Estimates Exact sciences and technology General mathematics General, history and biography Inequality Mathematical models Mathematics Mathematics and Statistics Sciences and techniques of general use Studies Symmetry Theorems |
| title | Dimension of quasicircles |
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