2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226214We 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 $1+k^2$.Acta Mathematica, to appearComplex Variables30C62; 30C80text