On $L^\infty $ estimates for complex Monge-Ampère equations


A PDE proof is provided for the sharp $L^\infty $ estimates for the complex Monge-Ampère equation that had required pluripotential theory before. The proof covers both cases of fixed background as well as degenerating background metrics. It extends to more general fully non-linear equations satisfying a structural condition, and it also gives estimates of Trudinger type.


Bin Guo

Department of Mathematics and Computer Science, Rutgers University, Newark, NJ

Duong H. Phong

Department of Mathematics, Columbia University, New York, NY

Freid Tong

Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA