The Douady-Earle extension of quasihomographies

Volume 37 / 1996

Ken-Ichi Sakan, Józef Zając Banach Center Publications 37 (1996), 35-44 DOI: 10.4064/-37-1-35-44


Quasihomography is a useful notion to represent a sense-preserving automorphism of the unit circle T which admits a quasiconformal extension to the unit disc. For K ≥ 1 let $A_T(K)$ denote the family of all K-quasihomographies of T. With any $f ∈ A_T(K)$ we associate the Douady-Earle extension $E_f$ and give an explicit and asymptotically sharp estimate of the $L_∞$ norm of the complex dilatation of $E_f$.


  • Ken-Ichi Sakan
  • Józef Zając

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