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The present volume is the first collection of surveys on Quasiconformal Space Mappings since the origin of the theory in and this collection provides in compact form access to a wide spectrum of recent results due to well-known specialists.

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Anderson, M. Vamanamurthy, M. Vuorinen: Conformal invariants, quasiconformal maps and special functions. Gehring: Topics in quasiconformal mappings.

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Iwaniec: L p -theory of quasiregular mappings. Martio: Partial differential equations and quasiregular mappings. Reshetnyak: On functional classes invariant relative to homothetics.

Rickman: Picard's theorem and defect relation for quasiconformal mappings. Srebro: Topological properties of quasiregular mappings.


Zorich: The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems. Namespaces Page Discussion. Views View View source History. Jump to: navigation , search. A numerical characterization of the distortion under a mapping at a point is the coefficient of quasi-conformality dilatation or dilation of at this point: The quantity is called the coefficient of quasi-conformality or linear dilatation of in the domain. Along with the given definition, one often uses the following, equivalent, conditions of quasi-conformality of in a domain : that is, has generalized derivatives that are locally -th power summable in and there exists a real number such that or for almost-all points.

How to Cite This Entry: Quasi-conformal mapping. Zorich originator , Encyclopedia of Mathematics. This page was last modified on 7 February , at Congress Mathematicians Helsinki, , Acad. Fennicae pp. Minnesota Ahlfors, L.

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Bers, "Riemann's mapping theorem for variable metrics" Ann. Belinskii, "General properties of quasi-conformal mappings" , Novosibirsk In Russian. Belinskii, "On the order of closeness of a spatial quasi-conformal mapping to conformal" Sibir. Nevanlinna ed. Press pp.

Bers, "Uniformization, moduli and Kleinian groups" Bull. London Math. Bers, "Quasi-conformal mappings with applications to differential equations, function theory and topology" Bull. Bers, "An extremal problem for quasi-conformal mappings and a problem of Thurston" Acta Math.

Beurling, L. Ahlfors, "The boundary correspondence under quasi-conformal mappings" Acta Math. Bojarski, T. Ivaniec, "Analytical foundations of the theory of quasi-conformal mappings in " Ann.

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AI Math. Caraman, " -dimensional quasi-conformal Qcf mappings" , Ed.

Drasin, "The inverse problem of Nevanlinna theory" Acta Math. Gehring, "Rings and quasiconformal mappings in space" Trans. Gehring, "Topics in quasiconformal mappings" , Proc. Congress Mathematicians Berkeley, , Amer. Gol'dshtein, "The behavior of mappings with bounded distortion when the coefficient of distortion is close to unity" Siber. Leipzig , 80 pp. Leipzig , 84 pp. Krushkal', R.

Nauk SSSR , 20 pp. Lavrent'ev] Lavrentieff, "The main theorem of the theory of quasi-conformal mappings of plain domains" Izv. Nauk SSSR , 12 pp.

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Lavrent'ev, "Variational methods for boundary value problems for systems of elliptic equations" , Noordhoff Translated from Russian. Lehto, K. Virtanen, "Quasiconformal mappings in the plane" , Springer Lichnerowicz " Acad. Martio, S. Rickman, J. Mostow, "Quasiconformal mappings in -space and the rigidity of hyperbolic space forms" Publ. IHES , 34 pp.

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Nevanlinna, "On differentiable mappings" R. Reshet'nyak, "Space mappings with bounded distortion" , Amer. Reshet'nyak, "Stability theorems in geometry and analysis" , Novosibirsk In Russian. Rickman, "On the number of omitted values of entire quasiregular mappings" J. Rickman, "The analogue of Picard's theorem for quasiregular mappings in dimension three" Acta Math.

Sullivan, "On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions" I. Kra ed. Maskit ed. Sullivan, "Quasi-conformal homeomorphisms and dynamics I. Solution of the Fatou—Julia problem on wandering domains" Ann. Sullivan, "Quasiconformal homeomorphisms and dynamics II. Structural stability implies hyperbolicity for Kleinian groups" Acta Math. Tukia, J. Vekua, "Generalized analytic functions" , Pergamon Translated from Russian.