{"paper":{"title":"Hardy inequalities on Riemannian manifolds and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lorenzo D'Ambrosio, Serena Dipierro","submitted_at":"2012-10-21T12:42:30Z","abstract_excerpt":"We prove a simple sufficient criteria to obtain some Hardy inequalities on Riemannian manifolds related to quasilinear second-order differential operator $\\Delta_{p}u := \\Div(\\abs{\\nabla u}^{p-2}\\nabla u)$. Namely, if $\\rho$ is a nonnegative weight such that $-\\Delta_{p}\\rho\\geq0$, then the Hardy inequality $$c\\int_{M}\\frac{\\abs{u}^{p}}{\\rho^{p}}\\abs{\\nabla \\rho}^{p} dv_{g} \\leq \\int_{M}\\abs{\\nabla u}^{p} dv_{g}, \\quad u\\in\\Cinfinito_{0}(M)$$ holds. We show concrete examples specializing the function $\\rho$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5723","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"}