Program
Some function theory on complete Kahler manifolds
Student No.:50
Time:Mon/Wed 15:10-17:00, 2015-06-17 ~ 2015-07-11
Instructor:Gang Liu  [University of California, Berkeley]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2015-6-17
Ending Date:2015-7-11
 

 

The lecture on July 13 will be change to July 11 at  10:10-12:00.

 

Description:

 

The uniformization conjecture of Yau states that a complete noncompact Kahler manifold with positive bisectional curvature is biholomorphic to the complex Euclidean space. This course introduces some function theory on complete Kahler manifolds with nonnegative bisectional curvature, with an aim at this conjecture.

 

 
Prerequisite:
 
Basic differential geometry, complex analysis

 

 

Reference:
 

We will not follow any textbook directly, but the following references will be useful.

1. N. Mok, Y. T. Siu and S. T. Yau, The Poincare-Lelong equation on complete Kahler manifolds, Compositio. Math(44), 1981, 183-218.

2. J. P. Demailly, Analytic methods in algebraic geometry, International press, 2010.

3. L. Ni and L. F. Tam, Plurisubharmonic functions and the structure of complete Kahler manifolds with nonnegative curvature, J. Diff. Geom(64), 2003, 457-524.

4. L. Ni, A monotonicity formula on complete Kahler manifolds with nonnegative bisectional curvature, J. Amer. Math. Soc 17(2004), no. 4, 909-946.

5. G. Liu,  Three circle theorems on Kahler manifolds and applications, arxiv: 1308. 0710.

6. R. Schoen and S. T. Yau, Lectures on differential geometry, International press, 1994.