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

  • Duong H. Phong EMAIL logo , Sebastien Picard and Xiangwen Zhang


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

Award Identifier / Grant number: DMS-12-66033

Award Identifier / Grant number: DMS-1308136

Funding statement: Work supported in part by the National Science Foundation under Grant DMS-12-66033 and DMS-1308136.


The authors would like to thank Pengfei Guan for stimulating conversations and for his notes on Fu–Yau’s equation. They would also like to thank Valentino Tosatti for his lectures and notes on Strominger systems. The authors are also very grateful to the referee for a particularly careful reading of the paper, and for numerous suggestions which helped clarify the paper a great deal.


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Received: 2016-01-18
Revised: 2016-03-25
Published Online: 2016-10-13
Published in Print: 2019-06-01

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