Geometric Function Theory
M.Phil/Ph.D Course
Geometric Function Theory
Area theorem, growth, distortion theorems, coefficient estimates for univalent functions special classes of univalent functions. Lowner’s theory and its applications; outline of de Banges proof of Bieberbach conjecture. Generalization of the area theorem, Grunsky inequalities, exponentiation of the Grunsky inequalities, Logarithmic coefficients. Subordination and Sharpened form of Schwarz Lemma
References
P. Duren, Univalent Functions, Springer, New York, 1983
A. W. Goodman, Univalent Functions I & II, Mariner, Florida, 1983
Ch. Pommerenke, Univalent Functions, Van den Hoek and Ruprecht, Göttingen, 1975.
M. Rosenblum, J. Rovnyak, Topics in Hardy Classes and Univalent Functions, Birkhauser Verlag, 1994
D. J. Hallenbeck, T. H. MacGregor, Linear Problems and Convexity Techniques in Geometric Function Theory, Pitman Adv. Publ. Program, Boston-London-Melbourne,1984.
I. Graham, G. Kohr, Geometric Function Theory in One and Higher Dimensions,Marcel Dekker, New York, 2003.