Local noncollapsing for complex Monge-Amp\`ere equations

Bin Guo; Jian Song

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arXiv · 2201.02930

Local noncollapsing for complex Monge-Amp\`ere equations

Bin Guo·Jian Song

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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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Bin Guo, Jian Song. 2022-01-09. Local noncollapsing for complex Monge-Amp\`ere equations. https://arxiv.org/abs/2201.02930

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