Uniform estimates for complex Monge-Ampere and fully nonlinear equations

Abstract:

Uniform estimates for the complex Monge Ampere equation has had a long history, starting with Yau’s famous resolution of the Calabi conjecture. Subsequent developments has led to many geometric applications and openings of new fields, but have all relied on the methods of pluripotential theory. In this talk, we will discuss a new PDE method of obtaining sharp uniform estimates for complex Monge-Ampere, without using pluripotential theory. This new methods extends more generally to other fully non-linear equations in complex geometry. This is based on joint work with B. Guo and D.H. Phong.