Geodesic
Axial Symmetry Indices for Convex Cones: Axiomatic Formalism and Applications
Journal of convex analysis, Tome 26 (2019) no. 1, pp. 217-244
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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.
Classification : 47L07, 52A20, 52A40, 52A41
Mots-clés : Convex cone, axially symmetric cone, axial symmetry index, generalized reflection matrix 
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     author = {A. Seeger and M. Torki},
     title = {Axial {Symmetry} {Indices} for {Convex} {Cones:} {Axiomatic} {Formalism} and {Applications}},
     journal = {Journal of convex analysis},
     pages = {217--244},
     year = {2019},
     volume = {26},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2019_26_1_JCA_2019_26_1_a12/}
}
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A. Seeger; M. Torki. Axial Symmetry Indices for Convex Cones: Axiomatic Formalism and Applications. Journal of convex analysis, Tome 26 (2019) no. 1, pp. 217-244. http://geodesic.mathdoc.fr/item/JCA_2019_26_1_JCA_2019_26_1_a12/