{ "id": "1311.7076", "version": "v2", "published": "2013-11-27T19:13:12.000Z", "updated": "2013-12-09T17:58:35.000Z", "title": "Reverse and dual Loomis-Whitney-type inequalities", "authors": [ "Stefano Campi", "Richard J. Gardner", "Paolo Gronchi" ], "categories": [ "math.MG" ], "abstract": "Various results are proved giving lower bounds for the $m$th intrinsic volume $V_m(K)$, $m=1,\\dots,n-1$, of a compact convex set $K$ in ${\\mathbb{R}}^n$, in terms of the $m$th intrinsic volumes of its projections on the coordinate hyperplanes (or its intersections with the coordinate hyperplanes). The bounds are sharp when $m=1$ and $m=n-1$. These are reverse (or dual, respectively) forms of the Loomis-Whitney inequality and versions of it that apply to intrinsic volumes. For the intrinsic volume $V_1(K)$, which corresponds to mean width, the inequality obtained confirms a conjecture of Betke and McMullen made in 1983.", "revisions": [ { "version": "v2", "updated": "2013-12-09T17:58:35.000Z" } ], "analyses": { "subjects": [ "52A20", "52A40", "52A38" ], "keywords": [ "dual loomis-whitney-type inequalities", "th intrinsic volume", "coordinate hyperplanes", "compact convex set", "giving lower bounds" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable", "adsabs": "2013arXiv1311.7076C" } } }