Hyperplane projections of the unit ball of ℓp n

F. Barthe, A. Naor

Research output: Contribution to journalArticle

Abstract

Let Bp n = {x ∈ℝni=1 n|xi|p ≤ 1}, 1 ≤ p ≤ + ∞. We study the extreme values of the volume of the orthogonal projection of Bp n onto hyperplanes H ℝ Rn. For a fixed H, we prove that the ratio vol(PHBp n)/vol(Bp n-1) is non-decreasing in p ∈ [1, +∞].

Original languageEnglish (US)
Pages (from-to)215-226
Number of pages12
JournalDiscrete and Computational Geometry
Volume27
Issue number2
StatePublished - 2002

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Orthogonal Projection
Extreme Values
Unit ball
Hyperplane
Projection

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology

Cite this

Hyperplane projections of the unit ball of ℓp n . / Barthe, F.; Naor, A.

In: Discrete and Computational Geometry, Vol. 27, No. 2, 2002, p. 215-226.

Research output: Contribution to journalArticle

Barthe, F & Naor, A 2002, 'Hyperplane projections of the unit ball of ℓp n ', Discrete and Computational Geometry, vol. 27, no. 2, pp. 215-226.
Barthe, F. ; Naor, A. / Hyperplane projections of the unit ball of ℓp n . In: Discrete and Computational Geometry. 2002 ; Vol. 27, No. 2. pp. 215-226.
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