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Journal of Convex Analysis 26 (2019), No. 1, 217--244
Copyright Heldermann Verlag 2019

Axial Symmetry Indices for Convex Cones: Axiomatic Formalism and Applications

Alberto Seeger
Dép. de Mathématiques, Université d'Avignon, 33 rue Louis Pasteur, 84000 Avignon, France

Mounir Torki
CERI, Université d'Avignon, 339 chemin de Meinajaries, 84911 Avignon, France

We address the issue of measuring the degree of axial symmetry of a convex cone. By following an axiomatic approach, we introduce and explore the concept of axial symmetry index. This concept is illustrated with the help of several interesting examples. By way of application, we establish a conic version of the Blekherman inequality concerning the quality of the approximation of a convex body by its inscribed ellipsoid.

Keywords: Convex cone, axially symmetric cone, axial symmetry index, generalized reflection matrix.

MSC: 47L07, 52A20, 52A40, 52A41

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