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A priori estimates and existence of solutions to the prescribed centroaffine curvature problem

Huaiyu Jian Jian Lu Xu-Jia Wang

Geometric Analysis and Geometric Topology mathscidoc:1910.43004

Journal of Functional Analysis, 274, (3), 826-862, 2018.2
In this paper we study the prescribed centroaffine curvature problem in the Euclidean space R n+ 1. This problem is equivalent to solving a Monge鈥揂mp猫re equation on the unit sphere. It corresponds to the critical case of the Blaschke鈥揝antal贸 inequality. By approximation from the subcritical case, and using an obstruction condition and a blow-up analysis, we obtain sufficient conditions for the a priori estimates, and the existence of solutions up to a Lagrange multiplier.
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@inproceedings{huaiyu2018a,
  title={A priori estimates and existence of solutions to the prescribed centroaffine curvature problem},
  author={Huaiyu Jian, Jian Lu, and Xu-Jia Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191007231312395378533},
  booktitle={Journal of Functional Analysis},
  volume={274},
  number={3},
  pages={826-862},
  year={2018},
}
Huaiyu Jian, Jian Lu, and Xu-Jia Wang. A priori estimates and existence of solutions to the prescribed centroaffine curvature problem. 2018. Vol. 274. In Journal of Functional Analysis. pp.826-862. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191007231312395378533.
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