Local noncollapsing for complex Monge-Ampère equations

Published 9 Jan 2022 in math.DG and math.AP | (2201.02930v2)

Abstract: 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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