## Abstract

We prove that for any two convex open bounded bodies K and T there exists a diffeomorphism f : K → T preserving volume ratio (i.e. with constant determinant of the Jacobian) and such that the Minkowski sum K + T { x + f (x) | x ∈ K }. As an application of this method, we prove some of the Alexandov–Fenchel inequalities.

Original language | American English |
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Pages (from-to) | 201-212 |

Number of pages | 12 |

Journal | Geometriae Dedicata |

Volume | 74 |

Issue number | 2 |

DOIs | |

State | Published - 1999 |

## Keywords

- Alexandrov-Fenchel inequalities
- Brenier map

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