Fu-Yau Hessian equation

Duong H. Phong Columbia University Sebastien Picard University of British Columbia Xiangwen Zhang University of California, Irvine

Analysis of PDEs Complex Variables and Complex Analysis Differential Geometry mathscidoc:2106.03001

We solve the Fu-Yau equation for arbitrary dimension and arbitrary slope $\alpha'$. Actually we obtain at the same time a solution of the open case $\alpha'>0$, an improved solution of the known case $\alpha'<0$, and solutions for a family of Hessian equations which includes the Fu-Yau equation as a special case. The method is based on the introduction of a more stringent ellipticity condition than the usual $\Gamma_k$ admissible cone condition, and which can be shown to be preserved by precise estimates with scale.
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  title={Fu-Yau Hessian equation},
  author={Duong H. Phong, Sebastien Picard, and Xiangwen Zhang},
Duong H. Phong, Sebastien Picard, and Xiangwen Zhang. Fu-Yau Hessian equation. 2018. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210602130458308329839.
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