{"paper":{"title":"A local proof of the dimensional Pr\\'ekopa's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Van Hoang Nguyen","submitted_at":"2014-04-17T13:47:34Z","abstract_excerpt":"The aim of this paper is to find an expression for second derivative of the function $\\phi(t)$ defined by $$\\phi(t) = \\lt(\\int_V \\vphi(t,x)^{-\\beta} dx\\rt)^{-\\frac1{\\be -n}},\\qquad \\beta\\not= n,$$ where $U\\subset \\R$ and $V\\subset \\R^n$ are open bounded subsets, and $\\vphi: U\\times V\\to \\R_+$ is a $C^2-$smooth function. As a consequence, this result gives us a direct proof of the dimensional Pr\\'ekopa's theorem based on a local approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4525","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"}