Rocky Mountain Journal of Mathematics

Slit univalent harmonic mappings

Armen Grigoryan

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In this paper we consider the class of complex-valued harmonic univalent functions that map the unit disc onto the complex plane, half-plane or a strip slit along finitely many horizontal half-lines.

Article information

Rocky Mountain J. Math., Volume 46, Number 1 (2016), 169-187.

First available in Project Euclid: 23 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

Univalent harmonic mappings boundary behavior of harmonic mappings


Grigoryan, Armen. Slit univalent harmonic mappings. Rocky Mountain J. Math. 46 (2016), no. 1, 169--187. doi:10.1216/RMJ-2016-46-1-169.

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  • L.V. Ahlfors, Complex Analysis, Third edition, McGraw-Hill, Inc., New York, 1979.
  • J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. 9 (1984), 3–25.
  • M. Dorff, M. Nowak and M. Wołoszkiewicz, Harmonic mappings onto parallel slit domains, Ann. Polon. Math. 101.2 (2011), 149–162.
  • T.A. Driscoll and L.N. Trefethen, Schwarz-Christoffel Mapping, Cambridge Mono. App. Comp. Math., Cambridge University Press, Cambridge, 2002.
  • P. Duren, Harmonic Mappings in the Plane, Cambridge University Press, Cambridge, 2004.
  • ––––, Univalent Functions, Springer-Verlag, New York, 1983.
  • A. Ganczar and J. Widomski, Univalent harmonic mappings into two-slit domains, J. Austral. Math. Soc. 88 (2010), 61–73.
  • A. Grigoryan and W. Szapiel, Two-slit harmonic mappings, Ann. Univ. Mariae Curie-Skłod. 49 (1995), 59–84.
  • ––––, An existence theorem for harmonic homeomorphisms with a given range and some convergence theorems, Complex Variab. Ellipt. Equat. 52 (2007), 341–350.
  • W. Hengartner and G. Schober, Univalent harmonic mappings, Trans. Amer. Math. Soc. 299 (1987), 1–31.
  • H. Lewy, On the non-vanishing of the Jacobian in certain one-to-one mappings, Bull. Amer. Math. Soc. 42 (1936), 689–692.
  • A.E. Livingston, Univalent harmonic mappings, Ann. Polon. Math. 57 (1992), 57–70.
  • ––––, Univalent harmonic mappings II, Ann. Polon. Math. 67 (1997), 131–145.
  • Ch. Pommerenke, Boundary behaviour of comformal maps, Springer-Verlag, New York, 1992.