On the approximation of a polytope by its dual $L_{p}$-centroid bodies Academic Article uri icon

abstract

  • We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P ∈ Rn by its dual L p-centroid bodies is independent of the geometry of P. In particular, we show that if P has volume 1, lim p→∞ p/log p (|Z pο(P)|/|Pο|-)= n2. We provide an application to the approximation of polytopes by uniformly convex sets.

author list (cited authors)

  • Paouris, G., & Werner, E.

citation count

  • 5

publication date

  • January 2013