Fu-Yau Hessian Equations

Duong H. Phong; Sebastien Picard; Xiangwen Zhang

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arXiv · 1801.09842

Fu-Yau Hessian Equations

Duong H. Phong·Sebastien Picard·Xiangwen Zhang

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Abstract

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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Duong H. Phong, Sebastien Picard, Xiangwen Zhang. 2018-01-30. Fu-Yau Hessian Equations. https://arxiv.org/abs/1801.09842

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