Abstract

Up to orthogonal transformation, a solid closed convex cone K in the Euclidean space Rn+1 is the epigraph of a nonnegative sublinear function f from Rn to R. This work explores the link between the geometric properties of K and the analytic properties of f. Part two of this article is published in this journal 19 (2012), Number 1.

Author information

Contact details are reproduced from the original publication and may be historical.

Keywords

  • Convex cone
  • epigraphical cone
  • sublinear function
  • inradius of a cone
  • solidity
  • pointedness
  • angular spectrum

Mathematics Subject Classification

46B10, 46B20, 52A41

Suggested citation

A. Seeger. “Epigraphical Cones I.” Journal of Convex Analysis 18 (2011), No. 4, 1171–1196.

Copyright Heldermann Verlag 2011