Harmonic extensions of quasisymmetric mappings

Abstract

Let Γ be a quasisymmetric automorphism of the unit circle and P _γ its Poisson extension to the unit disk Δ. Various properties of P _γ are estabhshed. Hyperbolic and euclidean distance, between E _γ(z) and P _γ(z), z ε δ, are estimated, where E _γ is the Douady-Earle quasiconformal extension of γ to Δ.

AMS No.:

• planar harmonic maps
• quasisymmetric functions
• quasiconformal extension
• Primary 30C55
• Secondary 30C62
• Secondary 30C75
• Secondary 31A05

^*This work was supported in part by KBN (Scientific Research Council) grant No. 2 PO3A-002-08.

^*This work was supported in part by KBN (Scientific Research Council) grant No. 2 PO3A-002-08.

Notes

^*This work was supported in part by KBN (Scientific Research Council) grant No. 2 PO3A-002-08.