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Articles

On distortion of harmonic measure under locally quasiconformal mappings

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Pages 1550-1564 | Received 29 Aug 2019, Accepted 08 May 2020, Published online: 29 May 2020

References

  • Nevanlinna R. Das harmonische Mass von Punktmengen und seine Anwendung in der Funktionentheorie. Stockholm: H. Ohlssons boktryckeri; 1935, p. 116–133. (Comptes rendus du huitième Congrès des mathématiciens scandinaves).
  • Garnett JB, Marshall DE. Harmonic measure. Cambridge: Cambridge University Press; 2005. p. 571.
  • Ahlfors LV. Conformal invariants. New York: McGraw-Hill; 1973. p. 157.
  • Beurling A. The collected works of arne beurling. In: Carleson L, et al., editor. Complex analysis. Vol. 1. Boston: Birkhäuser; 1989.
  • Betsakos D, Solynin AY. Extensions of Beurling's shove theorem for harmonic measure. Complex Variables Elliptic Equ. 2000;42:57–65.
  • Ahlfors LV. Untersuchungen zur Theorie der konformen Abbildung und der ganzen Funktion, Acta Soc. Sci. Fenn., N.S., 1930, 1, No. 9.
  • Anderson GD, Vamanamurthy MK, Vuorinen M. Conformal invariants, inequalities an quasiconformal maps. New York: John Wiley & Sons; 1997. p. 505.
  • Lehto O, Virtanen K. Quasiconformal mappings in the plane. 2nd ed. New York: Springer-Verlag; 1973. p. 260.
  • Vasil'ev A. Moduli of families of curves for conformal and quasiconformal mappings. Berlin: Springer; 2002.
  • Ahlfors LV. Lectures on quasiconformal mappings: second edition. Providence (RI): AMS; 2006, p. 162. (University Lecture Series; vol. 38).
  • Zhong L. Locally quasiconformal mappings and the dirichlet problem of degenerate elliptic equations. Complex Var Theor Appl Int J. 1993;23(3–4):231–247.
  • Graf SY. An analog of the schwarz lemma for locally quasiconformal automorphisms of the unit disk. Russ Math (Iz. VUZ). 2014;58(11):74–79. doi: 10.3103/S1066369X14110097
  • Gutlyanskii V, Martio O, Sugava T, Vuorinen M. On the degenerate beltrami equation. Trans Amer Math Soc. 2005;357:875–900. doi: 10.1090/S0002-9947-04-03708-0
  • Duren P. Harmonic mappings in the plane. Cambridge: Cambridge University Press; 2004. p. 214.
  • Bshouty D, Hengartner W. Univalent harmonic mappings in the plane. In: Kuhnau R, editor. The handbook of complex analysis: geometric function theory. Vol. 2. Amsterdam: Elsevier; 2005. p. 876.
  • Kelingos JA. Characterizations of quasiconformal mappings in terms of harmonic and hyperbolic measure. Ann Acad Sci Fenn Ser A I. 1965;368:16.
  • Goluzin GM. Geometric theory of functions of a complex variable. Providence (RI): American Mathematical Society; 1969. p. 676. (Translations of mathematical monographs).
  • Pommerenke C, Jensen G. Univalent functions. Göttingen: Vandenhoeck und Ruprecht; 1975. p. 376.

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