Hyperplane projections of the unit ball of ℓpn

F. Barthe; A. Naor

doi:10.1007/s00454-001-0066-3

Hyperplane projections of the unit ball of ℓ_pⁿ

F. Barthe
, A. Naor

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

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

Original language	English (US)
Pages (from-to)	215-226
Number of pages	12
Journal	Discrete and Computational Geometry
Volume	27
Issue number	2
DOIs	https://doi.org/10.1007/s00454-001-0066-3
State	Published - Mar 2002
Externally published	Yes

All Science Journal Classification (ASJC) codes

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

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10.1007/s00454-001-0066-3

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title = "Hyperplane projections of the unit ball of ℓpn",

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

author = "F. Barthe and A. Naor",

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AU - Naor, A.

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N2 - Let Bpn = {x ∈ℝn;Σi=1 n|xi|p ≤ 1}, 1 ≤ p ≤ + ∞. We study the extreme values of the volume of the orthogonal projection of Bpn onto hyperplanes H ℝ Rn. For a fixed H, we prove that the ratio vol(PHBpn)/vol(Bpn-1) is non-decreasing in p ∈ [1, +∞].

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

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DO - 10.1007/s00454-001-0066-3

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SP - 215

EP - 226

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 2

ER -

Hyperplane projections of the unit ball of ℓ_pⁿ

Abstract

All Science Journal Classification (ASJC) codes

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