Sections of the unit ball of Ipn

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Abstract

Let Bnp={(xi)∈RN; σi=li=n|xi|p⩽1}, 1+⩽p⩽+∞, and let Ek be a k-dimensional subspace of Rn; it is proved that if p ⩾ 2 (resp. ⩽) then vol(BpnEk) ⩾ vol(Bpk) (resp. ⩽). We give some applications to linear forms.

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Present address: UFR de Mathématiques, Université de Paris VII, 2 place Jussieu, 75251, Paris Cedex 05, France.