### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1974-1997 |

Number of pages | 24 |

Journal | Advances in Mathematics |

Volume | 231 |

Issue number | 3-4 |

DOIs | |

State | Published - Oct 2012 |

### Keywords

- Brunn-Minkowski inequality
- Brunn-Minkowski-Firey inequality
- Minkowski mixed-volume inequality
- Minkowski-Firey L -combinations

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Böröczky, K. J., Lutwak, E., Yang, D., & Zhang, G. (2012). The log-Brunn-Minkowski inequality.

*Advances in Mathematics*,*231*(3-4), 1974-1997. https://doi.org/10.1016/j.aim.2012.07.015