A note on the volume of sections of Bn

Let Bn p denote the unit ball in n p with p 1. We prove that Voln−1(H ∩ Bn p) (Voln(Bn p))(n−1)/n for any (n−1)-dimensional subspace H of Rn. This is a consequence of bounding the isotropy constant of Bn p above by 1/√12 and we show that one can replace 1/√12 by a possibly smaller number for n 2. © 2006 Elsevier Inc. All rights reserved