Lectures: Tuesdays 12.15–14.00 and Thursdays 14.15–16.00

Start: Tuesday, March 17, 2026

Exercises: Tuesdays, 14.15–16.00

Credit points: 5

Lecturer: Katrin Fässler

Course assistant: Abhishek Pandey

See also SISU page.

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​What is... a quasiconformal mapping? (text by Juha Heinonen in AMS Notices)

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​Study materials

[K] P. Koskela: Lectures on quasiconformal and quasisymmetric mappings (link)

 

Program

1. Conformal mappings [K, 11.1, Lem. 8.4, 11.2], [GMP, Thm 3.1.1], [M, 1]

2. Metric definition of quasiconformality [K, 1], [GMP, 6.2.1, Thm 6.6.29], [V, 16.1, 16.2]

3. From metrically quasiconformal to locally quasisymmetric [K, 2.1, 2.2]

4. Tools from real and harmonic analysis [K, 2.3, 2.4, 2.5, 2.6]

5. Basic properties of quasisymmetric mappings [K, 3, 10.4-10.9], [H, 10-12]

6. Gehring's lemma [K, 4.1, 4.2, 4.3]

7. The analytic definition of quasiconformality [K, 5]

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Exercises

1. Sheet 1

2. Sheet 2

3. Sheet 3

4. Sheet 4

5. Sheet 5

6. Sheet 6

7. Sheet 7

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Evaluation

There is no written course exam. The grade will be based on a final project and the exercises. The details depend on the number of participants and will be announced at the beginning of the course.

 

Further literature

• [GeMaPa] F. Gehring, G. J. Martin, B. P. Palka: An Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings; American Mathematical Soc., 2017

• [H] J. Heinonen: Lectures on Analysis on Metric Spaces; Springer, 2012

• [M] G. Martin: The Theory of Quasiconformal Mappings in Higher Dimensions, I

• [V] J. Väisälä: Lectures on n-Dimensional Quasiconformal Mappings; Springer, 2006