Univalent harmonic mappings II

• Autorzy: Albert E. Livingston
• Języki publikacji: EN

Abstrakty

EN

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 $f_z̅(0) = 0$.

Słowa kluczowe

EN

univalent harmonic mappings; coefficient bounds; distortion theorems

Kategorie tematyczne

• 31A05: Harmonic, subharmonic, superharmonic functions
• 30C55: General theory of univalent and multivalent functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 67
• Numer: 2
• Strony: 131-145

Daty

wydano

1997

otrzymano

1996-09-11

Twórcy

autor

Albert E. Livingston

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

Bibliografia

• [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.