Abstract

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.

Author information

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Keywords

  • Convex cone
  • axially symmetric cone
  • axial symmetry index
  • generalized reflection matrix

Mathematics Subject Classification

47L07, 52A20, 52A40, 52A41

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Suggested citation

A. Seeger, M. Torki. “Axial Symmetry Indices for Convex Cones: Axiomatic Formalism and Applications.” Journal of Convex Analysis 26 (2019), No. 1, 217–244. https://doi.org/10.68381/jca26013

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.