Univalent Functions-Selected Topics

Prof. Glenn Schober (auth.)9780387073910, 0-387-07391-4

Table of contents :
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