Rotationally symmetric solutions to the Lp-Minkowski problem

Jian Lu Xu-Jia Wang

TBD mathscidoc:1910.43001

Journal of Differential Equations, 254, (3), 983-1005, 2013.2
In this paper we study the L p-Minkowski problem for p=鈭n鈭1, which corresponds to the critical exponent in the Blaschke鈥揝antalo inequality. We first obtain volume estimates for general solutions, then establish a priori estimates for rotationally symmetric solutions by using a Kazdan鈥揥arner type obstruction. Finally we give sufficient conditions for the existence of rotationally symmetric solutions by a blow-up analysis. We also include an existence result for the L p-Minkowski problem which corresponds to the super-critical case of the Blaschke鈥揝antalo inequality.
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@inproceedings{jian2013rotationally,
  title={Rotationally symmetric solutions to the Lp-Minkowski problem},
  author={Jian Lu, and Xu-Jia Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191007203001423337530},
  booktitle={Journal of Differential Equations},
  volume={254},
  number={3},
  pages={983-1005},
  year={2013},
}
Jian Lu, and Xu-Jia Wang. Rotationally symmetric solutions to the Lp-Minkowski problem. 2013. Vol. 254. In Journal of Differential Equations. pp.983-1005. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191007203001423337530.
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