A third derivative estimate for Monge-Ampere equations with conic singularities

Gang Tian

doi:10.1007/s11401-017-1090-9

Chinese Annals of Mathematics, Series B ›› 2017, Vol. 38 ›› Issue (2) : 687 -694. DOI: 10.1007/s11401-017-1090-9

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A third derivative estimate for Monge-Ampere equations with conic singularities

Gang Tian ¹^,²^,^a

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Abstract

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 Monge-Ampere equations in the conic case. This C ^2,α-estimate was used by Jeffres-Mazzeo-Rubinstein in their proof of the existence of Kähler-Einstein metrics with conic singularities.

Keywords

Complex / Monge-Ampere / Conic / C ^α-estimate

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Gang Tian. A third derivative estimate for Monge-Ampere equations with conic singularities. Chinese Annals of Mathematics, Series B, 2017, 38(2): 687-694 DOI:10.1007/s11401-017-1090-9

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