Quasiconformal mappings in the plane, spring 2016
- The first lecture is on January 18, first Exercise class on January 28 (changed!).
Weeks 3-9 on Monday 12-14 and Wednesday 14-16 in room B322.
Weeks 11-18 on Monday 12-14 in room C122 (changed room!).
Easter holiday 24.-30.3.
The credit can be obtained by doing the exercises (at least 75%) for period III and by giving presentations in period IV.
For a comprehensive treatment, see the book (available as e-book from HY university network)
Astala-Iwaniec-Martin: Elliptic PDE's and Quasiconformal mappings in the plane. Princeton University, 2009.
Topics to be covered (period III): distortion theorems for conformal maps, quasisymmetry vs quasiconformality, basic properties of quasiconformal maps and the measurable Riemann mapping theorem.
Topics for period IV (student presentations):
- hyperbolic metric and Schwarz lemma
- holomorphic motions and the lambda-lemma
- Examples of holomorphic motions, change of Hausdorff dimension
- real and complex interpolation of L^p-spaces
- Interpolation lemma and higher integrability for quasiconformal maps
- Distortion of area and Hausdorff dimension under quasiconformal maps
- Dimension of quasicircles
No need to register in advance, just come to the first class.
Did you forget to register? What to do?
The solutions are to be submitted to Oleg Ivrii (mailbox on the 3rd floor or firstname.lastname@example.org) before each Exercise class.
Exercise classes (during period III)
Course feedback can be given at any point during the course. Click here.