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Complex Variables and Elliptic Equations
An International Journal
Volume 61, 2016 - Issue 6
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Articles

The Grunsky function and Carathéodory metric of Teichmüller spaces

Samuel L. KrushkalDepartment of Mathematics, Bar-Ilan University, 5290002Ramat-Gan, Israel.;Department of Mathematics, University of Virginia, Charlottesville, VA, 22904-4137USA.Correspondence[email protected]
Pages 803-816 | Received 08 Jun 2015, Accepted 02 Dec 2015, Published online: 11 Jan 2016

References

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  • Krushkal SL. Milin’s coefficients, complex geometry of Teichmüller spaces and variational calculus for univalent functions. Georgian Math. J. 2014;21:313–332.
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  • Gardiner FP, Lakic N. Quasiconformal Teichmüller Theory. Providence (RI): American Mathematical Society; 2000.
  • Royden HL. Automorphisms and isometries of Teichmüller space. Advances in the theory of Riemann surfaces. Vol. 66, Annals of Mathematics Studies. Princeton: Princeton University Press; 1971. pp. 369–383
  • Grunsky H. Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen. Math. Z. 1939;45:29–61.
  • Krushkal SL. Grunsky coefficient inequalities, Carathéodory metric and extremal quasiconformal mappings. Comment. Math. Helv. 1989;64:650–660.
  • Kühnau R. Verzerrungssätze und Koeffizientenbedingungen vom Grunskyschen Typ für quasikonforme Abbildungen. Math. Nachr. 1971;48:77–105.
  • Krushkal SL. Strengthened Grunsky and Milin inequalities. Contemp. Math. Forthcoming 2016.
  • Kühnau R. Wann sind die Grunskyschen Koeffizientenbedingungen hinreichend für Q-quasikonforme Fortsetzbarkeit? [When are the Grunsky coefficient conditions sufficient for Q-quasiconformal extendibility?] Comment. Math. Helv. 1986;61:290–307.
  • Krushkal SL. Quasiconformal mappings and Riemann surfaces. New York (NY): Wiley; 1979.
  • Krushkal SL, Kühnau R. Quasiconformal reflection coefficient of level lines. Contemp. Math. 2011;553:155–172.
  • Krushkal SL. Plurisubharmonic features of the Teichmüller metric. Publications de l’Institut Mathématique-Beograd, Nouvelle série. 2004;75:119–138.
  • Minda D. The strong form of Ahlfors’ lemma. Rocky Mountain J. Math. 1987;17:457–461.
  • Bers L. Fiber space over Teichmüller spaces. Acta Math. 1973;130:89–126.

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