A note on quasiconformal maps with Holder-continuous dilatation

摘要

Recently J. Mateu, J. Orobitg, and J. Verdera showed that a Holder continuous complex dilatation supported on smooth domains is a sufficient condition for the resulting quasiconformal map to be bi-Lipschitz. Their proof is analytic and based on properties of the Beurling-Ahlfors transform. We give an alternate, more geometric proof and use it to extend their result to supporting domains with positive angle corners. (C) 2014 Elsevier Masson SAS. All rights reserved.