Program
An Introduction to Canonical Metrics in Kähler Geometry
Student No.:40
Time:Mon & Wed 08:00-09:35, Sep.17-Dec.12
Instructor:张蓥莹Zhang Yingying  
Place:Conference Room 3, Jin Chun Yuan West Bldg.
Starting Date:2018-9-17
Ending Date:2018-12-12

Description:
Canonical metrics play an important role in understanding the geometry and topology of a given manifold. In this course, we will focus on the existence of Kähler-Einstein metrics, balanced metrics and constant scalar curvature Kähler metrics in Kähler geometry. Background materials on Kähler geometry will be provided.


Prerequisite:
One semester course on Riemannian Geometry and Partial Differential Equations.


Reference:
[1] R. Berman, S. Boucksom, V. Guedj, A. Zeriahi, A variational approach to complex Monge-Ampère equations. Publ. Math. Inst. Hautes Études Sci. 117 (2013), 179–245;
[2] H.-D. Cao, Deformation of Kähler metrics to Kähler-Einstein metrics on compact Kähler manifolds. Invent. Math. 81 (1985), no. 2, 359–372;
[3] S.K. Donaldson, Scalar curvature and projective embeddings. I. J. Differential Geom. 59 (2001), no. 3, 479–522;
[4] H. Luo, Geometric criterion for Gieseker-Mumford stability of polarized manifolds. J. Differential Geom. 49 (1998), no. 3, 577–599;
[5] S.-T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I. Comm. Pure Appl. Math. 31 (1978), no. 3, 339–411.