Search results for "Quasiconformal mapping"

Quasiconformal mappings and global integrability of the derivative

1991

Quasiextremal distance domains and extension of quasiconformal mappings

1985

Quasihyperbolic boundary conditions and capacity: Hölder continuity of quasiconformal mappings

2001

We prove that quasiconformal maps onto domains which satisfy a suitable growth condition on the quasihyperbolic metric are uniformly continuous when the source domain is equipped with the internal metric. The obtained modulus of continuity and the growth assumption on the quasihyperbolic metric are shown to be essentially sharp. As a tool, we prove a new capacity estimate.

Bi-Sobolev extensions

2022

We give a full characterization of circle homeomorphisms which admit a homeomorphic extension to the unit disk with finite bi-Sobolev norm. As a special case, a bi-conformal variant of the famous Beurling-Ahlfors extension theorem is obtained. Furthermore we show that the existing extension techniques such as applying either the harmonic or the Beurling-Ahlfors operator work poorly in the degenerated setting. This also gives an affirmative answer to a question of Karafyllia and Ntalampekos.

Analytic capacity and quasiconformal mappings with $W^{1,2}$ Beltrami coefficient

2008

We show that if $\phi$ is a quasiconformal mapping with compactly supported Beltrami coefficient in the Sobolev space $W^{1,2}$, then $\phi$ preserves sets with vanishing analytic capacity. It then follows that a compact set $E$ is removable for bounded analytic functions if and only if it is removable for bounded quasiregular mappings with compactly supported Beltrami coefficient in $W^{1,2}$.

Hölder continuity of Sobolev functions and quasiconformal mappings

1993

Quasiconformal mappings and F-harmonic measure

1983

Lectures on quasiconformal and quasisymmetric mappings

2009

Weighted Hardy Spaces of Quasiconformal Mappings

2019

We establish a weighted version of the $H^p$-theory of quasiconformal mappings.