Journal of Convex Analysis 23 (2016), No. 4, 947--980
Copyright Heldermann Verlag 2016
On Measures of Size for Convex Cones
Alberto Seeger
Dept. of Mathematics, University of Avignon, 33 rue Louis Pasteur, 84000 Avignon, France
alberto.seeger@univ-avignon.fr
By using an axiomatic approach we formalize the concept of size index for closed convex cones in the Euclidean space Rn. We review a dozen of size indices disseminated through the literature, commenting on the advantages and disadvantages of each choice.
Keywords: Convex cone, ellipsoidal cone, solid angle, maximal angle, ball-truncated volume, canonical volume, Gaussian width, statistical dimension.
MSC: 28A75, 51M25, 52A20, 52A40
[ Fulltext-pdf (256 KB)] for subscribers only.