## Convex and Discrete GeometryConvex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas. The book gives an overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers. It should also be of use to people working in other areas of mathematics and in the applied fields. |

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### Contents

1 | |

10 | 37 |

Convex Bodies 3 Convex Sets Convex Bodies and Convex Hulls | 41 |

11 | 60 |

Mixed Volumes and Quermassintegrals | 79 |

Valuations | 110 |

The BrunnMinkowski Inequality | 141 |

Symmetrization | 168 |

12 | 381 |

16 | 416 |

20 | 429 |

27 | 442 |

32 | 450 |

34 | 499 |

References | 513 |

35 | 514 |

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### Common terms and phrases

affine Alexandrov algorithm assume balls basis boundary Brunn–Minkowski inequality cl conv closed convex coefficients combinatorial concluding the proof conjecture consider contains convex body convex cone convex functions convex geometry convex lattice polytopes convex polytopes convex sets Corollary corresponding defined definite quadratic forms density differentiable dimension discs edges ellipsoid equality exterior normal face facets Fejes T´oth finite following result following statements formula geometry of numbers given graph Gruber halfspaces Hence holds implies induction intersection isoperimetric inequality isoperimetric quotient Jordan measurable lattice packing lattice polytopes Lemma matrix metric minimum Minkowski mixed volumes normal vector notion orthogonal polynomial positive definite quadratic problem proper convex body proper convex polytope properties Proposition prove the following quadratic forms quermassintegrals relative interior rigid motions Sect show the following space Steiner suitable support hyperplane surface area theory tiling translates valuation vertex vertices yields