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Smooth solutions to the Lp dual Minkowski problem

Chuanqiang Chen Zhejiang University of Technology Yong Huang Hunan University Yiming Zhao Massachusetts Institute of Technology

Convex and Discrete Geometry mathscidoc:1911.43008

Math. Ann., 373, 953-976, 2019
In this paper, we consider the L p dual Minkowski problem by geometric variational method. Using anisotropic Gauss–Kronecker curvature flows, we establish the existence of smooth solutions of the L p dual Minkowski problem when pq ≥ 0 and the given data is even. If f ≡ 1, we show under some restrictions on p and q that the only even, smooth, uniformly convex solution is the unit ball.
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@inproceedings{chuanqiang2019smooth,
  title={Smooth solutions to the Lp dual Minkowski problem},
  author={Chuanqiang Chen, Yong Huang, and Yiming Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191125140342302031518},
  booktitle={Math. Ann.},
  volume={373},
  pages={953-976},
  year={2019},
}
Chuanqiang Chen, Yong Huang, and Yiming Zhao. Smooth solutions to the Lp dual Minkowski problem. 2019. Vol. 373. In Math. Ann.. pp.953-976. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191125140342302031518.
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