## Convexity and its applications |

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### Contents

Convexity and Optimization in Discrete Structures | 9 |

Isoperimetric Inequalities | 30 |

Convex Bodies of Constant Width | 49 |

Copyright | |

11 other sections not shown

### Common terms and phrases

algebraic algebraic lattice algorithm Amer analogue Banach space Blaschke bodies of constant Borel boundary bounded centrally symmetric centroid Chakerian characterization circles closed convex combinatorial compact conjecture constant width convex bodies convex disk convex polytopes convex sets curvature measures deﬁned deﬁnition denote density diameter diametrical chord dimension ellipsoid equal Euler characteristic exists extension Fejes Toth ﬁeld ﬁnd ﬁnite ﬁrst ﬁxed formulas given Groemer Hadwiger Hungar hyperplane inﬁnite integral geometry intersection isoperimetric inequality Lemma linear metric Minkowski additive Minkowski spaces mixed volumes n-dimensional optimal oriented matroid orthogonal plane convex bodies point processes polygons polyhedra polynomial problem Proc projection proof proved quasi-nonexpansive quermassintegrals random set Reuleaux Reuleaux polygons Reuleaux triangle satisﬁes Schneider sets of constant simple valuation simplex sphere spherical stereology Studia Sci subset support function surface area theorem theory translation invariant valuation Uber vector space zonoids zonotopes