12. Geometric inequalities and equalities in...

CI-dessus: Inequalities and geometric equalities in $ℝ_{2}^{n}$

12.1 Brunn and Minkowski inequality

Theorem (inequality of Brunn (1887, 1889) and Minkowski (1897)). Let X and Y be two compact convex bodies of $ℝ_{2}^{n}$ . The following inequality is satisfied (p. 204 of

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Geometric inequalities and equalities in...: bodies associated with a convex body

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Bibliography

(1) - ALEXANDROV (A.D.) - Zur Theorie der gemischten Volumina von konvexen Körpern, II: Neue Ungleichungen zwischen den gemischten Volumina und ihre Anwendungen, - Matematicheskii Sbornik N. S. 2, pp. 1205-1238, (en russe avec un résumé en allemand) (1937).
(2) - ANCIAUX...

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