Univalent harmonic mappings II

Albert E. Livingston

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 2, page 131-145
  • ISSN: 0066-2216

Abstract

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

How to cite

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Albert E. Livingston. "Univalent harmonic mappings II." Annales Polonici Mathematici 67.2 (1997): 131-145. <http://eudml.org/doc/270739>.

@article{AlbertE1997,
abstract = {Let a < 0 < b and Ω(a,b) = ℂ - ((-∞, a] ∪ [b,+∞)) and U= z: |z| < 1. We consider the class $S_H (U,Ω(a,b))$ of functions f which are univalent, harmonic and sense-preserving with f(U) = Ω and satisfying f(0) = 0, $f_z(0) > 0$ and $f_z̅(0) = 0$.},
author = {Albert E. Livingston},
journal = {Annales Polonici Mathematici},
keywords = {univalent harmonic mappings; coefficient bounds; distortion theorems; univalent harmonic function; extremal functions},
language = {eng},
number = {2},
pages = {131-145},
title = {Univalent harmonic mappings II},
url = {http://eudml.org/doc/270739},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Albert E. Livingston
TI - Univalent harmonic mappings II
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 2
SP - 131
EP - 145
AB - Let a < 0 < b and Ω(a,b) = ℂ - ((-∞, a] ∪ [b,+∞)) and U= z: |z| < 1. We consider the class $S_H (U,Ω(a,b))$ of functions f which are univalent, harmonic and sense-preserving with f(U) = Ω and satisfying f(0) = 0, $f_z(0) > 0$ and $f_z̅(0) = 0$.
LA - eng
KW - univalent harmonic mappings; coefficient bounds; distortion theorems; univalent harmonic function; extremal functions
UR - http://eudml.org/doc/270739
ER -

References

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  1. [1] Y. Abu-Muhanna and G. Schober, Harmonic mappings onto convex domains, Canad. J. Math. 39 (1987), 1489-1530. Zbl0644.30003
  2. [2] J. A. Cima and A. E. Livingston, Integral smoothness properties of some harmonic mappings, Complex Variables Theory Appl. 11 (1989), 95-110. Zbl0724.30011
  3. [3] J. A. Cima and A. E. Livingston, Nonbasic harmonic maps onto convex wedges, Colloq. Math. 66 (1993), 9-22. Zbl0820.30015
  4. [4] J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3-25. Zbl0506.30007
  5. [5] W. Hengartner and G. Schober, Univalent harmonic functions, Trans. Amer. Math. Soc. 299 (1987), 1-31. 
  6. [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. Zbl0664.30012
  7. [7] A. E. Livingston, Univalent harmonic mappings, Ann. Polon. Math. 57 (1992), 57-70. 

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