Convex Geometry II. Distances and Measures, Approximation, Comparison and Symmetrisation : Extreme sets and stability of geometric inequalities

Extreme sets and stability of geometric inequalities
Convex Geometry II. Distances and Measures, Approximation, Comparison and Symmetrisation

Author : Jean-Charles PINOLI

Publication date: November 10, 2020 | Lire en français

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14. Extreme sets and stability of geometric inequalities

An extremal set for a geometric inequality (I) is a subset satisfying the corresponding equality relation (E).

Questions about extremal sets are important, but beyond the scope of this article; see for an introductory article in dimension 2.

The stability of a geometric property that characterizes a class of non-empty subsets of $ℝ_{2}^{n}$ convex and compact...

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Extreme sets and stability of geometric inequalities

(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)...

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