A note on the holomorphic invariants of Tian-Zhu.
A viscosity approach to degenerate complex Monge-Ampère equations
This is the content of the lectures given by the author at the winter school KAWA3 held at the University of Barcelona in 2012 from January 30 to February 3. The main goal was to give an account of viscosity techniques and to apply them to degenerate Complex Monge-Ampère equations.We will survey the main techniques used in the viscosity approach and show how to adapt them to degenerate complex Monge-Ampère equations. The heart of the matter in this approach is the “Comparison Principle" which allows...
Affine compact almost-homogeneous manifolds of cohomogeneity one
This paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem...
Asymptotics of complete Kähler-Einstein metrics – negativity of the holomorphic sectional curvature.