Abstract

Up to orthogonal transformation, a solid closed convex cone K in the Euclidean space Rn+1\mathbb{R}^{n+1} is the epigraph of a nonnegative sublinear function f from Rn\mathbb{R}^n to R\mathbb{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.

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Keywords

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

Mathematics Subject Classification

46B10, 46B20, 52A41

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Suggested citation

A. Seeger. “Epigraphical Cones I.” Journal of Convex Analysis 18 (2011), No. 4, 1171–1196. https://doi.org/10.68381/jca18070

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.