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Existence of solutions to the even dual minkowski problem

Yiming Zhao New York University

Analysis of PDEs Convex and Discrete Geometry mathscidoc:1908.03002

Journal of Differential Geometry, 110, (3), 543-572, 2018
Recently, Huang, Lutwak, Yang & Zhang discovered the duals of Federer’s curvature measures within the dual Brunn-Minkowski theory and stated the “Minkowski problem” associated with these new measures. As they showed, this dual Minkowski problem has as special cases the Aleksandrov problem (when the index is 0) and the logarithmic Minkowski problem (when the index is the dimension of the ambient space)—two problems that were never imagined to be connected in any way. Huang, Lutwak, Yang & Zhang established sufficient conditions to guarantee existence of solution to the dual Minkowski problem in the even setting. In this work, existence of solution to the even dual Minkowski problem is established under new sufficiency conditions. It was recently shown by B ̈or ̈oczky, Henk & Pollehn that these new sufficiency conditions are also necessary.
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@inproceedings{yiming2018existence,
  title={EXISTENCE OF SOLUTIONS TO THE EVEN DUAL MINKOWSKI PROBLEM},
  author={Yiming Zhao},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190820214942983507423},
  booktitle={Journal of Differential Geometry},
  volume={110},
  number={3},
  pages={543-572},
  year={2018},
}
Yiming Zhao. EXISTENCE OF SOLUTIONS TO THE EVEN DUAL MINKOWSKI PROBLEM. 2018. Vol. 110. In Journal of Differential Geometry. pp.543-572. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190820214942983507423.
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