MATS225 Quasiconformal Mappings (5–9 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024
Description
The equivalent metric and analytic definitions of quasiconformality and the basic properties of quasiconformal mappings, techniques from real and harmonic analysis, Sobolev spaces and PDE's which are necessary for the theory, reverse Holder 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.
Description of prerequisites
Measure and Integral Theory
Completion methods
Method 1
Evaluation criteria:
points from exercises and/or seminar presentation and/or exam, depending on the implementation of the course.
Select all marked parts
Method 2
Evaluation criteria:
final exam points
Select all marked parts
Parts of the completion methods
x
Teaching (5–9 cr)
Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
points from exercises and/or seminar presentation and/or exam, depending on the implementation of the course
Language:
English
Study methods:
lectures and exercises
x
Exam (5–9 cr)
Type:
Exam
Grading scale:
0-5
Evaluation criteria:
final exam points
Language:
English