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Constant Scalar metrics on Kahler manifolds
时间  Datetime
2017-08-03 16:00 — 17:00 
地点  Venue
Middle Lecture Room
报告人  Speaker
He, Weiyong
单位  Affiliation
University of Oregon
邀请人  Host
Lai, Mijia
报告摘要  Abstract

A central problem in Kahler geometry, proposed in 1980s by E. Calabi  is to study the existence of a constant scalar curvature metric on a compact Kahler manifold (within a fixed Kahler class). This is a generalization of classical constant Gaussian curvature on surfaces and includes the more famous Kahler-Einstein metrics for special cases (for example, Calabi-Yau manifolds). Since the introduction by Calabi in 1980s, it has been studied extensively and becomes a very fast-growing subject in Kahler geometry. We will summarize briefly Calabi’s problem program, and consider this problem from a point of view of (fourth order) elliptic PDE.  We define a notion of weak solution and prove it regularity. This answers in part a conjecture of Xiuxiong Chen. This is joint work with You Zeng from University of Rochester.