“signed” Riemannian metric on manifolds
Student No.:50
Time:Mon 09:00-12:00, 2017-02-20~ 2017-06-05 (No classes on public holidays)
Instructor:Guoyi Xu  [Tsinghua University]
Place:【Updated】Lecture Hall, Floor 3, Jin Chun Yuan West Building
Starting Date:2017-2-20
Ending Date:2017-6-5






This course focuses on the construction of Riemannian metric with signed curvature on manifolds. We will start from Schoen-Yau’s surgery (non-negative scalar curvature), Sha-Yang’s surgery (non-negative Ricci curvature), Lohkamp’s existence of non-positive Ricci curvature metric etc. The content of the course may change around our varying understanding and digging. The lecture notes will be distributed in the class, no textbook. Finally, this is not an "advance, broad, top” course, the math language and techniques in the course are elementary even for undergraduate students, although some ideas are deep.







One semester PDE and one semester Riemannian geometry is enough.







Schoen-Yau’s paper on scalar curvature, Sha-Yang’s paper on Ricci curvature, Lohkamp’s paper on Ricci curvature, the papers of Cheeger-Colding and the people following them.