QC maps in the plane, Fall 2016

Quasiconformal mappings in the plane, Fall 2016

Teaching

Lectures 48h, Thu 10-12 MaD381 and Fri 12-14 MaD259 starting 15.9. Weekly written exercise sets. Students submit solutions to exercises for grading. Tutoring for exercises Thu 8-10 MaD380 starting 22.9.

Requirements

Final grade pass/fail will be determined by the written exercise grades and participation activity. Final exam only for those students who request grading scale 0-5.

Prerequisites

MATS111+MATS112 Measure and Integration, MATS121+MATS122 Complex Analysis

We will cover the basic analytic and geometric theory of quasiconformal mappings and the Beltrami equation.

Exercise sets

Set 1, due 23.9.
Set 2, due 30.9.
Set 3, due 7.10.
Set 4, due 14.10.
Set 5, due 21.10.
Set 6, due 28.10.
Set 7, due 4.11.
Set 8, due 11.11.
Set 9, due 18.11.
Set 10, due 25.11.

Literature

For most parts we will follow Astala, Iwaniec, Martin: Elliptic Partial Differential Equations and Quasiconformal maps in the plane, Princeton University Press, 2009. Other monographs on the topic include Ahlfors: Lectures on Quasiconformal mappings, D. van Nostrand Co., 1966 and Lehto, Virtanen: Quasiconformal Mappings in the plane, Springer, 1973.