Differential Geometry Seminar
In a recent paper, "On L∞ estimates for complex Monge-Amp`ere equations", the authors give a new proof of the C^0 estimate for complex Monge-Ampere equations. The result also applies to sigma_k equations and similar equations satisfying some structural conditions. A key part of the approach is to compare the solution with the solutions to some auxiliary complex Monge-Ampere equations, which is a recent fundamental new idea. In this talk, I will report on my readings in the first part of the paper.