Univalent Functions - Selected Topics

Functions with positive real part....Pages 1-5
Special classes: convex, starlike, real, typically real, close-to-convex, bounded boundary rotation....Pages 6-26
The Pólya-Schoenberg conjecture....Pages 27-33
Representation of continuous linear functionals....Pages 34-38
Faber polynomials....Pages 39-47
Extremal length and equicontinuity....Pages 48-56
Compact families ℱ(D,ℓ 1 ,ℓ 2 ,P,Q) of univalent functions normalized by two linear functionals....Pages 57-64
Properties of extreme points for some compact families ℱ(D,ℓ 1 ,ℓ 2 ,P,Q)....Pages 65-78
Elementary variational methods....Pages 79-91
Application of Schiffer’s boundary variation to linear problems....Pages 92-111
Application to some nonlinear problems....Pages 112-127
Some properties of quasiconformal mappings....Pages 128-137
A variational method for q.c. mappings....Pages 138-146
Application to families of conformal and q.c. mappings....Pages 147-167
Sufficient conditions for q.c. extensions....Pages 168-171