Gao, Peng (2005) A Note on the Volume of Sections of Bⁿp. Research report collection, 8 (4).

Abstract

Let Bⁿp denote the unit ball in lⁿp with p ≥ 1. We prove that Voln₋₁(H ∩ Bnp) ≥ (Voln(Bnp))⁽ⁿ⁻¹⁾ for any (n−1)-dimensional subspace H of Rⁿ. This is a consequence of bounding the isotropy constant of Bⁿp above by 1/√12 and we show that one can replace 1/√12 by a possibly smaller number for n ≥ 2.

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