{"paper":{"title":"An example related to the slicing inequality for general measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Alexander Koldobsky, Bo'az Klartag","submitted_at":"2017-06-04T19:11:26Z","abstract_excerpt":"For $n\\in \\mathbb{N}$ let $S_n$ be the smallest number $S>0$ satisfying the inequality $$ \\int_K f \\le S \\cdot |K|^{\\frac 1n} \\cdot \\max_{\\xi\\in S^{n-1}} \\int_{K\\cap \\xi^\\bot} f $$ for all centrally-symmetric convex bodies $K$ in $\\mathbb{R}^n$ and all even, continuous probability densities $f$ on $K$. Here $|K|$ is the volume of $K$. It was proved by the second-named author that $S_n\\le 2\\sqrt{n}$, and in analogy with Bourgain's slicing problem, it was asked whether $S_n$ is bounded from above by a universal constant. In this note we construct an example showing that $S_n\\ge c\\sqrt{n}/\\sqrt{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01132","kind":"arxiv","version":3},"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"}