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arXiv · 1705.08634

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

Chao Li·Jiayu Li·Xi Zhang
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Abstract

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

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Chao Li, Jiayu Li, Xi Zhang. 2017-05-24. A $\mathcal C^{2,\alpha}$ estimate of the complex Monge-Amp\`ere equation. https://arxiv.org/abs/1705.08634

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