Harmonic functions on Riemannian manifolds
Student No.:40
Time:Tue 19:20-21:45
Instructor:Xu Guoyi  [Tsinghua University]
Place:Conference Room 3, Floor 2, Jinchun Yuan West Building
Starting Date:2017-9-19
Ending Date:2018-1-2

This course will be around the harmonic functions on complete (especially non-compact) Riemannian manifolds with non-negative Ricci curvature or sectional curvature. Instead of focusing the analytic property of harmonic functions, we will emphasize the application of harmonic functions in the study of the geometric structure of Riemannian manifolds and their topology property.


The work of Cheeger-Gromoll, Yau, S.Y.Cheng, Peter Li, Colding-Minicozzi, Cheeger-Colding will be the timeline of the course, the content of the course will vary according to the math background of the audience, but it will be different from the stuff I had taught in Tsinghua before, and will not depend on my former course either.


The lecture notes will be distributed in the class, no textbook. Finally, we will always try to avoid new concepts or fancy language in the instruction, so the deep part are the philosophy or ideas behind those “old-fashioned" geometric analysis discovery.