Fu-Yau Hessian Equations

Original · EN

We solve the Fu-Yau equation for arbitrary dimension and arbitrary slope α'. Actually we obtain at the same time a solution of the open case α'>0, an improved solution of the known case α'<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 Γₖ admissible cone condition, and which can be shown to be preserved by precise estimates with scale.