WIAS Preprint No. 1476, (2010)

On properties of different notions of centers for convex cones



Authors

  • Henrion, René
  • Seeger, Alberto

2010 Mathematics Subject Classification

  • 46B10 46B20 52A41

Keywords

  • Convex cone, central axis, solidity coefficient, sharpness coefficient, revolution cone, ball-generated cone, geometry of Banach spaces

Abstract

The points on the revolution axis of a circular cone are somewhat special: they are the "most interior'' elements of the cone. This paper addresses the issue of formalizing the concept of center for a convex cone that is not circular. Four distinct proposals are studied in detail: the incenter, the circumcenter, the inner center, and the outer center. The discussion takes place in the context of a reflexive Banach space.

Appeared in

  • Set-Valued Var. Anal., 18 (2010) pp. 205--231.

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