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.