Abstract

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.

Author information

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Keywords

  • Convex cone
  • axially symmetric cone
  • axial symmetry degree
  • generalized reflection matrices

Mathematics Subject Classification

47L07, 52A20, 52A40, 52A41

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Suggested citation

A. Seeger, M. Torki. “Measuring Axial Symmetry in Convex Cones.” Journal of Convex Analysis 25 (2018), No. 3, 983–1011. https://doi.org/10.68381/jca25063

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press LLC.