MATS225 Quasiconformal Mappings (5–9 cr)
Description
Equivalent metric and analytic definitions of quasiconformality and basic properties of quasiconformal mappings, techniques from real and harmonic analysis, Sobolev spaces and PDEs that are necessary for the theory, reverse Hölder inequalities.
Learning outcomes
The students are introduced to the theory of quasiconformal (in the metric and analytic sense) and quasisymmetric maps. They know prototypical examples of such maps and their basic properties. Main topics are "local-to-global" results and the regularity of quasiconformal maps. Along the way, the students get acquainted with important tools from geometric and harmonic analysis, such as Poincaré inequalities and covering theorems.
Additional information
The number of credits for the course is 5 cr or 9 cr depending on the implementation.
Description of prerequisites
Measure and Integration Theory 1 and 2
Study materials
Lecture notes or other study materials will be announced separately.