Math 532A: Geometric Function Theory

Steffen Rohde

Winter 2001, Monday/Wednesday/Friday 10:30-11:20


Geometric function theory originated in the study of conformal maps of the unit disc, but has meanwhile spread into many different branches of mathematics. In this course, we will follow the historical development and first study conformal maps of the disc (distortion theorems, continuity up to the boundary), then discuss conformal invariants (hyperbolic metric, harmonic measure, extremal length) and finally develop the theory of quasiconformal maps. Many of these results and notions will be applied in the course Complex Dynamics (Math 533A, Spring 2000).

If time allows, we will also discuss the 'circle packing theorem' and other algorithms related to numerical conformal mapping.

There will be no textbook, as we will draw from various sources. I have put several books on reserve in the math library. To make life easier, I will hand out short notes (containing the definitions, theorems, and references).

Prerequisites: Complex Analysis (Math 534,535). For the second half of the course, some background in either Real or Linear Analysis would be helpful, but familiarity with the Lebesgue integral and Lp-spaces should be sufficient.