{"paper":{"title":"A Dimension-Free Hermite-Hadamard Inequality via Gradient Estimates for the Torsion Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Jianfeng Lu, Stefan Steinerberger","submitted_at":"2019-05-08T17:07:04Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^n$ be a convex domain and let $f:\\Omega \\rightarrow \\mathbb{R}$ be a subharmonic function, $\\Delta f \\geq 0$, which satisfies $f \\geq 0$ on the boundary $\\partial \\Omega$. Then $$ \\int_{\\Omega}{f ~dx} \\leq |\\Omega|^{\\frac{1}{n}} \\int_{\\partial \\Omega}{f ~d\\sigma}.$$ Our proof is based on a new gradient estimate for the torsion function, $\\Delta u = -1$ with Dirichlet boundary conditions, which is of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03216","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"}