Analysis Seminar

We will motivative the conjectures of Kobayashi, Lang, and Yau on various characterizations of positive canonical bundle over a projective manifold. Then we will provide a purely analytic proof of Yau's conjecture that if the manifold has negative holomorphic sectional curvature, then its canonical bundle is ample. If time permits, we shall extend the argument to complete Kahler manifolds.

This talk is based on the joint work with Yau.