Distortion function and quasisymmetric mappings

• Autorzy: J. Zając
• Języki publikacji: EN

Abstrakty

EN

We study the relationship between the distortion function $Φ_K$ and normalized quasisymmetric mappings. This is part of a new method for solving the boundary values problem for an arbitrary K-quasiconformal automorphism of a generalized disc on the extended complex plane.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991
• Tom: 55
• Numer: 1
• Strony: 361-369

Daty

wydano

1991

otrzymano

1990-09-12

Twórcy

autor

J. Zając

• Institute of Mathematics, Polish Academy of Sciences, Łódź Branch, Narutowicza 56, 90-136 Łódź, Poland

Bibliografia

• [AVV1] G. D. Anderson, M. K. Vamanamurphy and M. Vuorinen, Distortion function for plane quasiconformal mappings, Israel J. Math. 62 (1) (1988), 1-16.
• [AVV2] G. D. Anderson, M. K. Vamanamurphy and M. Vuorinen, Functional inequalities for hypergeometric and related functions, Univ. of Auckland, Rep. Ser. 242, 1990.
• [BA] A. Beurling and L. V. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 125-142.
• [HP] J. Hersch et A. Pfluger, Généralisation du lemme de Schwarz et du principe de la mesure harmonique pour les fonctions pseudo-analytiques, C. R. Acad. Sci. Paris 234 (1952), 43-45.
• [H] O. Hübner, Remarks on a paper by Ławrynowicz on quasiconformal mappings, Bull. Acad. Polon. Sci. 18 (1980), 183-186.
• [Ke] J. A. Kelingos, Boundary correspondence under quasiconformal mappings, Michigan Math. J. 13 (1966), 235-249.
• [Kr1] J. G. Krzyż, Quasicircles and harmonic measure, Ann. Acad. Sci. Fenn. 12 (1987), 19-24.
• [Kr2] J. G. Krzyż, Harmonic analysis and boundary correspondence under quasiconformal mappings, ibid. 14 (1989), 225-242.
• [LV] O. Lehto and K. I. Virtanen, Quasiconformal Mappings in the Plane, 2nd ed., Grundlehren Math. Wiss. 126, Springer, New York 1973.
• [W] C.-F. Wang, On the precision of Mori's theorem in Q-mappings, Science Record 4 (1960), 329-333.
• [Z] J. Zając, The distortion function $Φ_K$ and quasihomographies, in: Space Quasiconformal Mappings, A collection of surveys 1960-1990, Springer, to appear