Fu Yau Hessian equations
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.