Local noncollapsing for complex Monge-Amp\`ere equations

Bin Guo; Jian Song

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Local noncollapsing for complex Monge-Amp\`ere equations

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arxiv 2201.02930 v2 pith:JX3DVRU6 submitted 2022-01-09 math.DG math.AP

Bin Guo , Jian Song This is my paper · ORCID

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keywords localestimatecomplexequationsmonge-ampnoncollapsingvolumeahler

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We prove a local volume noncollapsing estimate for K\"ahler metrics induced from a family of complex Monge-Amp\`ere equations, assuming a local Ricci curvature lower bound. This local volume estimate can be applied to establish various diameter and gradient estimate.

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