The log-Brunn-Minkowski inequality

Károly J. Böröczky Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences Erwin Lutwak New York University Deane Yang New York University Gaoyong Zhang New York Uiversity

Convex and Discrete Geometry mathscidoc:1703.40008

Advances in Mathematics, 231, 1974–1997, 2012
For origin-symmetric convex bodies (i.e., the unit balls of finite dimensional Banach spaces) it is conjectured that there exist a family of inequalities each of which is stronger than the classical Brunn–Minkowski inequality and a family of inequalities each of which is stronger than the classical Minkowski mixed-volume inequality. It is shown that these two families of inequalities are “equivalent” in that once either of these inequalities is established, the other must follow as a consequence. All of the conjectured inequalities are established for plane convex bodies.
Brunn–Minkowski inequality; Brunn–Minkowski–Firey inequality; Minkowski mixed-volume inequality; Minkowski–Firey Lp-combinations
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@inproceedings{károly2012the,
  title={The log-Brunn-Minkowski inequality},
  author={Károly J. Böröczky, Erwin Lutwak, Deane Yang, and Gaoyong Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170302051456763043587},
  booktitle={Advances in Mathematics},
  volume={231},
  pages={1974–1997},
  year={2012},
}
Károly J. Böröczky, Erwin Lutwak, Deane Yang, and Gaoyong Zhang. The log-Brunn-Minkowski inequality. 2012. Vol. 231. In Advances in Mathematics. pp.1974–1997. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170302051456763043587.
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