Koebe distortion theorem

Theorem (Koebe).

Suppose f is a schlicht functionMathworldPlanetmath (univalent function on the unit discPlanetmathPlanetmath such that f(0)=0 and f(0)=1) then




Equality holds for one of the four inequalities at some point z0 if and only if f is a rotation of the Koebe function.


If K is a compact subset of a region GC, then there is a constant M (depending on K) such that for every univalent function f on G and ever pair of points z,wK we have



  • 1 John B. Conway. . Springer-Verlag, New York, New York, 1995.
Title Koebe distortion theorem
Canonical name KoebeDistortionTheorem
Date of creation 2013-03-22 14:23:25
Last modified on 2013-03-22 14:23:25
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 7
Author jirka (4157)
Entry type Theorem
Classification msc 30C45
Synonym distortion theorem
Synonym generalized distortion theorem
Synonym Köbe distortion theorem
Related topic SchlichtFunctions