The Douady-Earle extension of quasihomographies

Ken-Ichi Sakan; Józef Zając

Banach Center Publications (1996)

  • Volume: 37, Issue: 1, page 35-44
  • ISSN: 0137-6934

Abstract

top
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 .

How to cite

top

Sakan, Ken-Ichi, and Zając, Józef. "The Douady-Earle extension of quasihomographies." Banach Center Publications 37.1 (1996): 35-44. <http://eudml.org/doc/208614>.

@article{Sakan1996,
abstract = {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 $E_f$.},
author = {Sakan, Ken-Ichi, Zając, Józef},
journal = {Banach Center Publications},
keywords = {quasihomography; automorphism; Douady-Earle extension},
language = {eng},
number = {1},
pages = {35-44},
title = {The Douady-Earle extension of quasihomographies},
url = {http://eudml.org/doc/208614},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Sakan, Ken-Ichi
AU - Zając, Józef
TI - The Douady-Earle extension of quasihomographies
JO - Banach Center Publications
PY - 1996
VL - 37
IS - 1
SP - 35
EP - 44
AB - 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 $E_f$.
LA - eng
KW - quasihomography; automorphism; Douady-Earle extension
UR - http://eudml.org/doc/208614
ER -

References

top
  1. [DE] A. Douady and C.I. Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math. 157 (1986), 23-48. Zbl0615.30005
  2. [K] J.G. Krzyż, Quasicircles and harmonic measure, Ann. Acad. Sci. Fenn. 12 (1987), 19-24. Zbl0563.30016
  3. [LP] A. Lecko and D. Partyka, An alternative proof of a result due to Douady and Earle, Ann. Univ. Mariae Curie-Skłodowska Sectio A 42 (1988), 59-68. Zbl0712.30040
  4. [P1] D. Partyka, The maximal dilatation of Douady and Earle extension of a quasisymmetric automorphism of the unit circle, Ann. Univ. Mariae Curie-Skłodowska Sectio A 44 (1990), 45-57. 
  5. [P2] D. Partyka, A distortion theorem for quasiconformal automorphisms of the unit disc, Ann. Polon. Math. 55 (1991), 277-281. Zbl0759.30009
  6. [P3] D. Partyka, The maximal value of the function [ 0 ; 1 ] ∋ r ↦ Φ K 2 ( √ r ) - r , Bull. Soc. Sci. Lettres Łódź 45 Sér. Rech. Déform. 20 (1995), 49-55. 
  7. [Z1] J. Zając, The distortion function Φ K and quasihomographies, Current Topics of Analytic Function Theory, (1992), 403-428. 
  8. [Z2] J. Zając, Quasihomographies, Monograph, Preprint. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.