Univalent Functions - Selected Topics

Functions with positive real part.- Special classes: convex, starlike, real, typically real, close-to-convex, bounded boundary rotation.- The Pólya-Schoenberg conjecture.- Representation of continuous linear functionals.- Faber polynomials.- Extremal length and equicontinuity.- Compact families ?(D,?1,?2,P,Q) of univalent functions normalized by two linear functionals.- Properties of extreme points for some compact families ?(D,?1,?2,P,Q).- Elementary variational methods.- Application of Schiffer’s boundary variation to linear problems.- Application to some nonlinear problems.- Some properties of quasiconformal mappings.- A variational method for q.c. mappings.- Application to families of conformal and q.c. mappings.- Sufficient conditions for q.c. extensions.