English

A $\mathcal C^{2,\alpha}$ estimate of the complex Monge-Amp\`ere equation

Differential Geometry 2017-05-25 v1

Abstract

In this paper, we prove a C2,α\mathcal C^{2,\alpha}-estimate for the solution to the complex Monge-Amp\`ere equation det(uijˉ)=f\det(u_{i\bar{j}})=f with 0<fCα0< f\in \mathcal C^{\alpha}, under the assumption that uC1,βu\in \mathcal C^{1,\beta } for some β<1\beta <1 which depends on nn and α\alpha .

Keywords

Cite

@article{arxiv.1705.08634,
  title  = {A $\mathcal C^{2,\alpha}$ estimate of the complex Monge-Amp\`ere equation},
  author = {Chao Li and Jiayu Li and Xi Zhang},
  journal= {arXiv preprint arXiv:1705.08634},
  year   = {2017}
}