Abstract
Let B p n ={x∈\R n ;\; \sum i=1 n |x i | p ≤ 1} , 1≤ p\le+∈fty . We study the extreme values of the volume of the orthogonal projection of B p n onto hyperplanes H\subset \R n . For a fixed H , we prove that the ratio vol(P H B p n )/ vol(B p n-1 ) is non-decreasing in p∈[1,+∈fty] .
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Received May 21, 2001, and in revised form September 2, 2001. Online publication December 17, 2001.
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Barthe, F., Naor, A. Hyperplane projections of the unit ball of ℓ p n . Discrete Comput Geom 27, 215–226 (2002). https://doi.org/10.1007/s00454-001-0066-3
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DOI: https://doi.org/10.1007/s00454-001-0066-3