Fu-Yau Hessian Equations

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 ${\alpha }^{\prime }>0$, an improved solution of the known case ${\alpha }^{\prime }<0$, 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.

36 pages

References in corpus (7)

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• A class of curvature type equations
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• Parabolic complex Monge-Ampere equations on compact Kahler manifolds
• Regularity of Degenerate Hessian Equation
• Fully nonlinear equations of Krylov type on Riemannian manifolds with negative curvature
• A class of prescribed Weingarten curvature equations in Euclidean space