Univalent harmonic mappings

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

Abstrakty

EN

Let a < 0, Ω = ℂ -(-∞, a] and U = {z: |z| < 1}. We consider the class $S_H(U,Ω)$ of functions f which are univalent, harmonic and sense preserving with f(U) = Ω and satisfy f(0) = 0, $f_z(0) > 0$ and $f_{z̅}(0) = 0$. We describe the closure $\overline{S_H(U,Ω)}$ of $S_H(U,Ω)$ and determine the extreme points of $\overline{S_H(U,Ω)}$.

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: 1992
• Tom: 57
• Numer: 1
• Strony: 57-70

Daty

wydano

1992

otrzymano

1991-01-14

poprawiono

1991-07-05

Twórcy

autor

Albert E. Livingston

• Department of Mathematical Sciences, University of Delaware, 501 Ewing Hall, 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 11 (1989), 95-110.
• [3] J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. AI 9 (1984), 3-25.
• [4] D. J. Hallenbeck and T. H. MacGregor, Linear Problems and Convexity Techniques in Geometric Function Theory, Monographs and Studies in Math. 22, Pitman, 1984.
• [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, Birkhäuser, 1988, 87-100.
• [7] W. Szapiel, Extremal problems for convex sets. Applications to holomorphic functions, Dissertation XXXVII, UMCS Press, Lublin 1986 (in Polish).