The author applies the arguments in his PKU Master degree thesis in 1988 to derive a third derivative estimate, and consequently, a C2,α-estimate, for complex Monge-Ampere equations in the conic case. This C2,α-estimate was used by Jeffres-Mazzeo-Rubinstein in their proof of the existence of Kähler-Einstein metrics with conic singularities.
Complex Monge-Ampere Conic Cα-estimate
2000 MR Subject Classification
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Jeffres, T., Mazzeo, R. and Rubinstein, Y., Kähler-Einstein metrics with edge singularities (with an appendix by C. Li and Y. Rubinstein), Annals of Math., 183, 2016, 95–176.MathSciNetCrossRefMATHGoogle Scholar