{"paper":{"title":"On the reverse Loomis-Whitney inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Paolo Gronchi, Peter Gritzmann, Stefano Campi","submitted_at":"2016-07-25T12:50:13Z","abstract_excerpt":"The present paper deals with the problem of computing (or at least estimating) the LW-number $\\lambda(n)$, i.e., the supremum of all $\\gamma$ such that for each convex body $K$ in $\\mathbb{R}^n$ there exists an orthonormal basis $\\{u_1,\\ldots,u_n\\}$ such that $$ vol_n(K)^{n-1} \\geq \\gamma \\prod_{i=1}^n vol_{n-1} (K|u_i^{\\perp}) , $$ where $K|u_i^{\\perp}$ denotes the orthogonal projection of $K$ onto the hyperplane $u_i^{\\perp}$ perpendicular to $u_i$. Any such inequality can be regarded as a reverse to the well-known classical Loomis--Whitney inequality. We present various results on such reve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07891","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}