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

By Duong H. Phong, Sebastien Picard, Xiangwen Zhang. Journal für die Reine und Angewandte Mathematik, 2015

71 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5d25b51145e9f369889a96923b2e585a5448803c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Zhizhang Wang
2. Changyu Ren
3. Xiangwen Zhang
4. Pengfei Guan
5. Duong H. Phong
6. Valentino Tosatti
7. B. Weinkove
8. Sebastien Picard

In Mathematical Physics

1. Xiangwen Zhang
2. Zhizhang Wang
3. Changyu Ren
4. Pengfei Guan
5. Duong H. Phong
6. Sebastien Picard

In Statistical and Nonlinear Physics

1. Xiangwen Zhang

Citations in the corpus

• The global curvature estimate for the n-2 Hessian equation (2020, background): “Phong-Picard-Zhang [36, 37] has considered Fu-Yau equation in high dimensional spaces, which is a complex 2Hessian equation with the right hand side function depending on the gradient term.”
• A class of curvature type equations. (2019, background): “There have been a lot of works related to this equation recently, see for example, Fu-Yau [16, 17] and Phong-Picard-Zhang [40, 41, 42].”