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

2015/07/29 by Phong, Duong H., Picard, Sebastien, Zhang, Xiangwen
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1507.08193

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 C⁰, C² and C^2,α a priori estimates. We also identify difficulties in extending the Fu-Yau arguments for non-degeneracy from dimension 2 to higher dimensions.

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• The Fu-Yau equation in higher dimensions
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• Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4