{"paper":{"title":"A remark on the slicing problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Apostolos Giannopoulos, Beatrice-Helen Vritsiou, Grigoris Paouris","submitted_at":"2011-07-22T14:31:13Z","abstract_excerpt":"The purpose of this article is to describe a reduction of the slicing problem to the study of the parameter I_1(K,Z_q^o(K))=\\int_K ||< :, x> ||_{L_q(K)}dx. We show that an upper bound of the form I_1(K,Z_q^o(K))\\leq C_1q^s\\sqrt{n}L_K^2, with 1/2\\leq s\\leq 1, leads to the estimate L_n\\leq \\frac{C_2\\sqrt[4]{n}log(n)} {q^{(1-s)/2}}, where L_n:= max {L_K : K is an isotropic convex body in R^n}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4527","kind":"arxiv","version":1},"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"}