{"paper":{"title":"Remarks on the KLS conjecture and Hardy-type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"Alexander V. Kolesnikov, Emanuel Milman","submitted_at":"2014-05-03T19:04:07Z","abstract_excerpt":"We generalize the classical Hardy and Faber-Krahn inequalities to arbitrary functions on a convex body $\\Omega \\subset \\mathbb{R}^n$, not necessarily vanishing on the boundary $\\partial \\Omega$. This reduces the study of the Neumann Poincar\\'e constant on $\\Omega$ to that of the cone and Lebesgue measures on $\\partial \\Omega$; these may be bounded via the curvature of $\\partial \\Omega$. A second reduction is obtained to the class of harmonic functions on $\\Omega$. We also study the relation between the Poincar\\'e constant of a log-concave measure $\\mu$ and its associated K. Ball body $K_\\mu$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0617","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"}