Bernstein theorem and regularity for a class of monge-amp`ere equations

Huaiyu Jian Tsinghua University Xu-Jia Wang Australian National University

Differential Geometry mathscidoc:1609.10305

Journal of Differential Geometry, 93, (3), 431-469, 2013
In this paper we first introduce a transform for convex functions and use it to prove a Bernstein theorem for a Monge-Amp`ere equation in half space.We then prove the optimal global regularity for a class of Monge-Amp`ere type equations arising in a number of geometric problems such as Poincar´e metrics, hyperbolic affine spheres, and Minkowski type problems.
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@inproceedings{huaiyu2013bernstein,
  title={BERNSTEIN THEOREM AND REGULARITY FOR A CLASS OF MONGE-AMP`ERE EQUATIONS},
  author={Huaiyu Jian, and Xu-Jia Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914074524727478967},
  booktitle={Journal of Differential Geometry},
  volume={93},
  number={3},
  pages={431-469},
  year={2013},
}
Huaiyu Jian, and Xu-Jia Wang. BERNSTEIN THEOREM AND REGULARITY FOR A CLASS OF MONGE-AMP`ERE EQUATIONS. 2013. Vol. 93. In Journal of Differential Geometry. pp.431-469. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914074524727478967.
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