# Univalent harmonic mappings II

Annales Polonici Mathematici (1997)

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

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topAlbert 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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- [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] J. A. Cima and A. E. Livingston, Nonbasic harmonic maps onto convex wedges, Colloq. Math. 66 (1993), 9-22. Zbl0820.30015
- [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] 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. Zbl0664.30012
- [7] A. E. Livingston, Univalent harmonic mappings, Ann. Polon. Math. 57 (1992), 57-70.

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