Until further notice, this course is organized through remote teaching so that you can study at home. Please contact the lecturer if you plan to follow the course but have not registered.

 

Lecture: Tuesdays and Thursdays, 14:15-16:00

Start: Tuesday, March 17, 2020

Exercises: Mondays, 14:15-16:00

Credit points: 5

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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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Lectures are available on nextcloud. Please contact the lecturer for the access link. There is also a discussion forum and chat available on moodle. To join those, you have to register for the course on SISU.

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Exercises

1. Sheet 1

2. Sheet 2

3. Sheet 3

4. Sheet 4

5. Sheet 5

6. Sheet 6

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Study materials

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

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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