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The logarithmic Minkowski problem

Károly J. Böröczky Alfréd Rényi Institute of Mathematics Erwin Lutwak New York University Deane Yang New York University Gaoyong Zhang New York University

Analysis of PDEs Differential Geometry Convex and Discrete Geometry mathscidoc:1702.03082

Journal of the American Mathematical Society, 26, (3), 831–852, 2013
In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the unit ball of a finite dimensional Banach space.
cone-volume measure, Minkowski problem, L p -Minkowski problem, log- Minkowski problem
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@inproceedings{károly2013the,
  title={The logarithmic Minkowski problem},
  author={Károly J. Böröczky, Erwin Lutwak, Deane Yang, and Gaoyong Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228044536689699541},
  booktitle={Journal of the American Mathematical Society},
  volume={26},
  number={3},
  pages={831–852},
  year={2013},
}
Károly J. Böröczky, Erwin Lutwak, Deane Yang, and Gaoyong Zhang. The logarithmic Minkowski problem. 2013. Vol. 26. In Journal of the American Mathematical Society. pp.831–852. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170228044536689699541.
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