Abstract
We solve the Fu–Yau equation for arbitrary dimension and arbitrary slope $\alpha^\prime$. Actually we obtain at the same time a solution of the open case $\alpha^\prime \gt 0$, an improved solution of the known case $\alpha^\prime \lt 0$, 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.
Funding Statement
Work supported in part by the National Science Foundation Grants DMS-12-66033 and the Simons Collaboration Grant for Mathematicians: 523313.
Citation
Duong H. Phong. Sebastien Picard. Xiangwen Zhang. "Fu–Yau Hessian equations." J. Differential Geom. 118 (1) 147 - 187, May 2021. https://doi.org/10.4310/jdg/1620272943
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