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Journal of Convex Analysis 25 (2018), No. 3, 983--1011
Copyright Heldermann Verlag 2018

Measuring Axial Symmetry in Convex Cones

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

The problem of measuring the degree of central symmetry of a convex body has been treated by various authors since the early twentieth century. This work addresses the issue of measuring the degree of axial symmetry of a convex cone. Passing from central symmetry in convex bodies to axial symmetry in convex cones is not a mere routine. Although it is possible to push the parallelism between both issues at a great level of generality, there are a number of substantial differences as well.

Keywords: Convex cone, axially symmetric cone, axial symmetry degree, generalized reflection matrices.

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

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