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Article | REF: AF220 V1

Convex Geometry II. Distances and Measures, Approximation, Comparison and Symmetrisation

Author: Jean-Charles PINOLI

Publication date: November 10, 2020

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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 ℝ2n convex and compact can be expressed as follows (p. 227 of

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Extreme sets and stability of geometric inequalities
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