DOI: 10.1112/jlms.70753 ISSN: 0024-6107

Restricted hyperplane sections of the cross‐polytope and the simplex

Silouanos Brazitikos, Christos Pandis
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Abstract

We give a new proof of Webb's theorem on maximal central hyperplane sections of the regular ‐simplex , viewed in its standard embedding in . A similar method also yields sharp maximal estimates for noncentral sections of whose distance from the barycenter is small, namely . Moreover, we obtain sharp volume estimates for central hyperplane sections of the cross‐polytope that pass through the barycenter of a facet.

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