Kaisa_2012_3_photo by Veikko Somerpuro

The course is an introduction to the theory of planar quasiconformal mappings, their analytic and geometric properties and their interactions with PDE's.
Schedule: Lectures Tue 10-12 B322, Wed 10-12 C323, Exercise class: Mon 12-14 C322 (N.B. no exercise class on 3.9.2018, first lecture on 4.9.2018!)

Enrol
13.8.2018 at 09:00 - 17.10.2018 at 23:59

Timetable

Here is the course’s teaching schedule. Check the description for possible other schedules.

DateTimeLocation
Mon 3.9.2018
12:15 - 14:00
Tue 4.9.2018
10:15 - 12:00
Wed 5.9.2018
10:15 - 12:00
Mon 10.9.2018
12:15 - 14:00
Tue 11.9.2018
10:15 - 12:00
Wed 12.9.2018
10:15 - 12:00
Mon 17.9.2018
12:15 - 14:00
Tue 18.9.2018
10:15 - 12:00
Wed 19.9.2018
10:15 - 12:00
Mon 24.9.2018
12:15 - 14:00
Tue 25.9.2018
10:15 - 12:00
Wed 26.9.2018
10:15 - 12:00
Mon 1.10.2018
12:15 - 14:00
Tue 2.10.2018
10:15 - 12:00
Wed 3.10.2018
10:15 - 12:00
Mon 8.10.2018
12:15 - 14:00
Tue 9.10.2018
10:15 - 12:00
Wed 10.10.2018
10:15 - 12:00
Mon 15.10.2018
12:15 - 14:00
Tue 16.10.2018
10:15 - 12:00
Wed 17.10.2018
10:15 - 12:00

Material

Here you will find some relevant study material such as lecture notes and links to literature.

A comprehensive treatment of the subject is the monograph Elliptic partial differential equations and quasiconformal mappings in the plane by K. Astala, T. Iwaniec and G. Martin (link to e-book accessible from HY network). Parts of Chapters 1-5 are relevant for this course.

Lecture material

Tasks

Exercise set 1

This is the first exercise set. We will discuss the solutions on the September 17 Exercise class. Return your answers before the class.

Istvan Prause

Exercise set 2

The second exercise set is due by September 24.

Istvan Prause

Exercise set 3

Exercise set 3 is due by 1.10.2018

Istvan Prause

Exercise set 4

The Exercise set 4 is due by October 8.

Istvan Prause

Exercise set 5

The final exercise set is due by October 15.

Istvan Prause

Conduct of the course

The course can be completed by solving the exercises. The solutions should be returned to Istvan Prause (mailbox on the 3rd floor or by email istvan.prause@helsinki.fi) by the indicated deadline. You can also hand in the solutions at the beginning of the exercise class.

Description

Real analysis
Complex analysis I, Functional analysis
Introduction to the theory of planar quasiconformal mappings, their analytic and geometric properties and their interactions with PDE's
1. or 2. year
Distortion theorems for conformal maps. Quasisymmetry versus quasiconformality, geometric versus analytic properties. Basic properties of quasiconformal maps, Lusin's condition N, Hölder continuity. Beurling transform, Beltrami equation and the measurable Riemann mapping theorem.
Exam and exercises, other methods will be described later
Lecture notes
Lectures and exercise classes
Exam and excercises, Course will be graded with grades 1-5
Exam and exercises, other methods will be described later