A Third Derivative Estimate for Monge-Ampere Equations with Conic Singularities(Dedicated to Haim Brezis on the occasion of his 70th birthday)

摘要

The author applies the arguments in his PKU Master degree thesis in 1988 to derive a third derivative estimate, and consequently, a C^(2,α)-estimate, for complex MongeAmpere equations in the conic case. This C^(2,α)-estimate was used by Jeffres-MazzeoRubinstein in their proof of the existence of K¨ahler-Einstein metrics with conic singularities.