MAT 627: Quasiconformal mappings

Spring 2018

Christopher Bishop

Professor, Mathematics
SUNY Stony Brook

Office: 4-112 Mathematics Building
Phone: (516)-632-8274
Dept. Phone: (516)-632-8290
FAX: (516)-632-7631

ORIGINAL TIME/PLACE: TuTh 10:00am - 11:20am, Physics P-122

NEW TIME/PLACE: Th 9:00am - 11:20am, Math 5-127

The classs time was changed because the orginal time coincided with MAT 555 (Lyubich) and MAT 656 (Bedford), class of interest to the same students as mine.

I am trying to write some lecture notes to go along with the class. The current version is posted here . This file will be updated throughout the semester.

Introduction to the course

Quasiconformal maps in the plane are a generalziation of conformal maps where we allw angles to be distorted in a bounded way. Such maps share several properties with conformal maps, but are much more flexible, easier to create and maniputlate, and the definition can be extended to more general metric spaces.

In this course we will cover the basic properties planar quasiconformal maps. Much of what we do overlaps with Ahlfors' book "Lectures on Quasiconformal Mappings", but I will often try to give a more detailed proof than what is written in Ahlfors' terse book.

We will start with a chapter on extrmeal length, then one of the geometric definition of quasiconformal maps, including a weak version of meaureable Riemann mapping theorem that is adequate for some applications in dynamics, and finish with a third chapter on analytic properties of quasiconformal mappings. If time permits, I will include a few applications of these ideas, such as Kesten's upper bound on the growth of DLA, Sullivan's non-wandering domain theorem and the construction of some entire functions with exotic dynamical properties.

Tentative Lecture Schedule

Thursday, Jan 25 Introduction, Extremal length
Thursday, Feb 2 no class
Thursday, Feb 9 Logarithmic capacity
Thursday, Feb 15 no class
Thursday, Feb 22
Thursday, Feb 22

Send the lecturer (C. Bishop) email at: bishop - at -