Crash-course on quasi-conformal mappings

I intend to give a short (i.e. 4 lectures) introductionary course on quasi-conformal mappings.
We will discuss concepts such as: extremal length, modulus, Koebe functions, Mori's Theorem, Quasi-conformal reflections, the Beltrami equation, Teichmuller spaces, Quasi-regular mappings (in higher dimensions), and maybe even the Loewner differential equation.

There will be two lectures a week during two weeks:
Thursday March 30, Friday March 31, Thursday April 6, and Friday April 7.
The time slot is the unusual 9-11 (or more precisely 09.00 to 10.45),
and the place is Mallvinden.
Modulus
Reference book/lecture notes,
Lars V. Ahlfors, Lectures on Quasiconformal Mappings, Wadsworth & Brook/Cole, 1966, 1987.
Lectures by V. Markovic and notes taken by A. Fletcher both of Warwick University, 2003.

Wellcome,
Torbjörn Lundh


Thursday, March 30

Introduction
(See also Alexander Vasil'ev's historical background,
 i.e. the introduction to his book Moduli of Families of Curves for Conformal and Quasiconformal Mappings, LNM 1788, Springer, 2002)
  • Grötzsch's problem: How to map a square to a rectangle?
  • The Riemann Mapping Theorem
  • A discrete version
  • The complex dilatation
  • Definition of K-qc
  • Solution to Grötzsch's problem

 Friday, March 31

Continuation
  • Composed mappings
  • Teichmuller distance
  • Extremal length
                                                        
Thursday, March 6
  • Modulus
  • Quasi-invariance of the extremal length


 Friday, March 7
  • Mori's Theorem
  • The Beltrami equation
  • Quadrilaterals to quadilaterals
  • Teichmuller's extremal theorem
  • Quasi regular mappings