On estimates for the Fu-Yau generalization of a Strominger system

Abstract

We study an equation proposed by Fu and Yau as a natural $n$-dimensional generalization of a Strominger system that they solved in dimension $2$. It is a complex Hessian equation with right hand side depending on gradients. Building on the methods of Fu and Yau, we obtain $C^0$, $C^2$ and $C^{2,\alpha }$ a priori estimates. We also identify difficulties in extending the Fu-Yau arguments for non-degeneracy from dimension $2$ to higher dimensions.

34 pages, final version, to appear in Crelle's Journal

References in corpus (2)

• Weak solutions of complex Hessian equations on compact Hermitian manifolds
• On uniform estimate of complex elliptic equations on closed Hermitian manifolds

Cited by in corpus (8)

• Weak solutions of complex Hessian equations on compact Hermitian manifolds
• Fu-Yau Hessian Equations
• New curvature flows in complex geometry
• Geometric flows and Strominger systems
• A flow of conformally balanced metrics with Kähler fixed points
• The Anomaly flow on unimodular Lie groups
• A second order estimate for general complex Hessian equations
• The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary