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The Lp-Alekesandrov problem for Lp-integral curvature

Yong Huang Hunan university Erwin Lutwak New York University Deane Yang New York University Gaoyong Zhang New York University

Differential Geometry mathscidoc:1911.10001

J. Differential Geom., 110, (1), 1-29, 2018
It is shown that within the Lp-Brunn–Minkowski theory that Aleksandrov’s integral curvature has a natural Lp extension, for all real p. This raises the question of finding necessary and sufficient conditions on a given measure in order for it to be the Lp-integral curvature of a convex body. This problem is solved for positive p and is answered for negative p provided the given measure is even.
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@inproceedings{yong2018the,
  title={ The Lp-Alekesandrov problem for Lp-integral curvature},
  author={Yong Huang, Erwin Lutwak, Deane Yang, and Gaoyong Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191125141144462160519},
  booktitle={ J. Differential Geom.},
  volume={110},
  number={1},
  pages={1-29},
  year={2018},
}
Yong Huang, Erwin Lutwak, Deane Yang, and Gaoyong Zhang. The Lp-Alekesandrov problem for Lp-integral curvature. 2018. Vol. 110. In J. Differential Geom.. pp.1-29. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191125141144462160519.
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