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Quasiconformal extensions of starlike harmonic mappings in the unit disc

손광호|Hidetaka Hamada|Tatsuhiro Honda
대한수학회 (The Korean Mathematical Society)|2013.07|대한수학회보 (Bulletin of the KMS)|제50권 제4호|pp. 1377-1387

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참고문헌

키워드

harmonic mappingquasiconformal extensionstarlike domain
주제분류수학

초록

Let f be a harmonic mapping on the unit disc Δ in C. We give some condition for f to be a quasiconformal homeomorphism on Δ and to have a quasiconformal extension to the whole plane C. We also obtain quasiconformal extension results for starlike harmonic mappings of order α∈2 (0, 1).

Abstract

Let f be a harmonic mapping on the unit disc Δ in C. We give some condition for f to be a quasiconformal homeomorphism on Δ and to have a quasiconformal extension to the whole plane C. We also obtain quasiconformal extension results for starlike harmonic mappings of order α∈2 (0, 1).

참고문헌 (17)

  1. L. V. Ahlfors, "Quasiconformal reflections", Acta Math, 109, pp.291~301 (1963)
  2. Y. Avcıand, "On harmonic univalent mappings", Ann. Univ. Mariae Curie- Sk lodowska Sect. A, 44, pp.13~7 (1990)
  3. A. A. Brodskiı, "Quasiconformal extension of biholomorphic mappings, Theory of mappings and approximation of functions, In Naukova Dumka", pp.30~34 (1983), Kiev
  4. P. Curt, "Homeomorphic extension of strongly spirallike mappings in Cn", Sci. China. Math, 53(1), pp.87~100 (2010)
  5. J. Clunie, "Harmonic univalent functions", Ann. Acad. Sci. Fenn. Ser. A. I Math, 9, pp.3~25 (1984)
  6. M. Fait, "Explicit quasiconformal extensions for some classes of univalent functions", Comment. Math. Helv, 51(2), pp.279~285 (1976)
  7. A. Ganczar, "On harmonic univalent mappings with small coefficients", Demonstratio Math, 34(3), pp.549~558 (2001)
  8. A. Ganczar, "Explicit quasiconformal extensions of planar harmonic mappings", J. Comput. Anal. Appl, 10(2), pp.179~186 (2008)
  9. I. Graham, "Radius problems for holomorphic mappings on the unit ball in Cn", Math. Nachr, 279(13), pp.1474~1490 (2006)
  10. H. Hamada, "Loewner chains and quasiconformal extension of holomorphic mappings", Ann. Polon. Math, 81(1), pp.85~100 (2003)
  11. H. Hamada, "Quasiconformal extension of biholomorphic mappings in several complex variables", J. Anal. Math, 96, pp.269~282 (2005)
  12. H. Hamada, "Univalence criterion and quasiconformal extension of holomorphic mappings", Manuscripta Math, 141(1), pp.195~209 (2013)
  13. J. M. Jahangiri, "Harmonic functions starlike in the unit disk", J. Math. Anal. Appl, 235(2), pp.470~477 (1999)
  14. O. Lehto, "Quasiconformal Mappings in the Plane" (1973), Springer-Verlag
  15. H. Lewy, "On the non-vanishing of the Jacobian in certain one-to-one mappings", Bull. Amer. Math. Soc, 42(10), pp.689~692 (1936)
  16. T. Sheil-Small, "Complex Polynomials, Cambridge Studies in Advanced Mathematics, 75" (2002), Cambridge University Press
  17. H. Silverman, "Harmonic univalent functions with negative coefficients", J. Math. Anal. Appl, 220(1), pp.283~289 (1998)

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