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On $L^\infty$ estimates for complex Monge-Amp\`ere equations

Differential Geometry 2021-06-07 v1 Analysis of PDEs

Abstract

A PDE proof is provided for the sharp LL^\infty estimates for the complex Monge-Amp\`ere equation which had required pluripotential theory before. The proof covers both cases of fixed background as well as degenerating background metrics. It extends to more general fully non-linear equations satisfying a structural condition, and it also gives estimates of Trudinger type.

Keywords

Cite

@article{arxiv.2106.02224,
  title  = {On $L^\infty$ estimates for complex Monge-Amp\`ere equations},
  author = {Bin Guo and Duong H. Phong and Freid Tong},
  journal= {arXiv preprint arXiv:2106.02224},
  year   = {2021}
}

Comments

24 pages

R2 v1 2026-06-24T02:49:23.963Z