Geometric estimates for complex Monge-Ampere equations

Bin Guo; Jian Song; Xin Fu

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Geometric estimates for complex Monge-Ampere equations

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arxiv 1706.01527 v1 pith:DK6THMNW submitted 2017-06-05 math.DG math.AP

Xin Fu , Bin Guo , Jian Song This is my paper · ORCID

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keywords complexequationsestimatesgeometricmonge-amperediameterproveuniform

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We prove uniform gradient and diameter estimates for a family of geometric complex Monge-Ampere equations. Such estimates can be applied to study geometric regularity of singular solutions of complex Monge-Ampere equations. We also prove a uniform diameter estimate for collapsing families of twisted Kahler-Einstein metrics on Kahler manifolds of nonnegative Kodaira dimensions.

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