English

Local noncollapsing for complex Monge-Amp\`ere equations

Differential Geometry 2022-10-04 v2 Analysis of PDEs

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.

Keywords

Cite

@article{arxiv.2201.02930,
  title  = {Local noncollapsing for complex Monge-Amp\`ere equations},
  author = {Bin Guo and Jian Song},
  journal= {arXiv preprint arXiv:2201.02930},
  year   = {2022}
}

Comments

Minor revision

R2 v1 2026-06-24T08:43:54.141Z