Quasiconformal and harmonic maps on surfaces
Student No.:80
Time:Mon 09:50-11:25 & 13:30-15:05, Jul.9/16/23/30
Instructor:罗峰 Luo Feng  
Place:Lecture Hall, 3rd floor of Jin Chun Yuan West Bldg.
Starting Date:2018-7-9
Ending Date:2018-7-30

This is an introductory lecture on quasiconformal and harmonic maps between surfaces. We will begin with the definitions of quasiconformal and harmonic maps and end with the proof of the analytic and geometric properties of these maps. The main theorems to be proved are: the measurable Riemann mapping theorem, the existence and uniqueness of and harmonic maps onto Riemannian surface of negative curvature and Schoen-Yau’s theorem on the diffeomorphic property of harmonic maps. Other topics will be covered if time permits. The lectures will be complementary to Professors L. Ji and K. Liu’s courses.

1. Ahlfors, L, Lectures on Quasiconformal mappings;
2. Lehto and Virtanen, quasiconformal mappings in the plane;
3. Jost, J., Compact Riemann surfaces (for harmonic maps).