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
alberto.seeger@univ-avignon.fr
Mounir Torki
CERI, Université d'Avignon, 339 Chemin de Meinajaries, 84911 Avignon, France
mounir.torki@univ-avignon.fr
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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