6 papers · 1 filter
Improved regularity of harmonic diffeomorphic extensions on quasihyperbolic domains
Zhuang Wang, Haiqing Xu
Let be a Jordan domain satisfying hyperbolic growth conditions. Assume that is a homeomorphism from the boundary of onto the uni…
Generalized quasidisks and conformality: progress and challenges
Chang-Yu Guo, Haiqing Xu
In this notes, we survey the recent developments on theory of generalized quasidisks. Based on the more or less standard techniques used earlier, we also provide some minor improve…
Optimal extensions of conformal mappings from the unit disk to cardioid-type domains
Haiqing Xu
The conformal mapping from onto the standard cardioid has a homeomorphic extension of finite distortion to entire We study the optimal…
Weighted estimates for diffeomorphic extensions of homeomorphisms
Haiqing Xu
Let $Ω\subset \mbr^2$ be an internal chord-arc domain and $φ: \mbs^1 \rightarrow \partial Ω$ be a homeomorphism. Then there is a diffeomorphic extension $h : \mbd \rightarrow Ω$ of…
Controlled diffeomorphic extension of homeomorphisms
Pekka Koskela, Zhuang Wang, Haiqing Xu
Let be an internal chord-arc Jordan domain and be a homeomorphism. We show that has finite dyadic energy if and only if has a diffeomo…
Planar mappings of subexponentially integrable distortion -- integrability of distortion of inverses
Haiqing Xu
We establish the optimal regularity for the distortion of inverses of mappings of finite distortion with logarithm-iterated style subexponentially integrable distortion, which gene…