【摘要】
Searching for canonical metrics on compact Kahler manifolds is one of the central problems in geometric analysis. In this talk we will focus on the existence problem of constant scalar curvature Kahler (csck) metrics. The (still open) Yau-Tian-Donaldson conjecture predicts that existence of cscK metrics is equivalent to K stability. Using quantization techniques, we introduce another stability notion, called K-beta stability. We show that this new stability notion is purely algebraic and is equivalent to the existence of cscK metrics. This talk is based on my joint work with T. Darvas.
