Dimension of quasicircles
Abstract
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 $1+k^2$.
 Publication:

arXiv eprints
 Pub Date:
 April 2009
 arXiv:
 arXiv:0904.1237
 Bibcode:
 2009arXiv0904.1237S
 Keywords:

 Mathematics  Complex Variables;
 30C62;
 30C80
 EPrint:
 Acta Mathematica, to appear