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ArticleOriginal scientific text

Title

Univalent harmonic mappings II

Authors 1

Affiliations

  1. Department of Mathematics University of Delaware Newark, Delaware 19716 U.S.A.

Abstract

Let a < 0 < b and Ω(a,b) = ℂ - ((-∞, a] ∪ [b,+∞)) and U= {z: |z| < 1}. We consider the class SH(U,Ω(a,b)) of functions f which are univalent, harmonic and sense-preserving with f(U) = Ω and satisfying f(0) = 0, fz(0)>0 and fz̅(0)=0.

Keywords

ENG
univalent harmonic mappings, coefficient bounds, distortion theorems

Bibliography

  1. Y. Abu-Muhanna and G. Schober, Harmonic mappings onto convex domains, Canad. J. Math. 39 (1987), 1489-1530.
  2. J. A. Cima and A. E. Livingston, Integral smoothness properties of some harmonic mappings, Complex Variables Theory Appl. 11 (1989), 95-110.
  3. J. A. Cima and A. E. Livingston, Nonbasic harmonic maps onto convex wedges, Colloq. Math. 66 (1993), 9-22.
  4. J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3-25.
  5. W. Hengartner and G. Schober, Univalent harmonic functions, Trans. Amer. Math. Soc. 299 (1987), 1-31.
  6. W. Hengartner and G. Schober, Curvature estimates for some minimal surfaces, in: Complex Analysis, J. Hersch and A. Huber (eds.), Birkhäuser, 1988, 87-100.
  7. A. E. Livingston, Univalent harmonic mappings, Ann. Polon. Math. 57 (1992), 57-70.
Annales Polonici Mathematici
1997/67/2
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Pages:
131-145
Main language of publication
English
Received
1996-09-11
Published
1997
Exact and natural sciences