11. Geometric inequalities and equalities in...

Above: Inequalities and geometric equalities in $ℝ_{2}^{3}$

11.1 Minkowski inequalities

Theorem (quadratic and cubic inequalities of Minkowski (1903)). Let X be a non-empty compact subset of $ℝ_{2}^{3}$ . The two Minkowski's quadratic inequalities are (p. 116 of

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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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