{"paper":{"title":"Hardy and Hardy-Sobolev inequalities on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"El Hadji Abdoulaye Thiam","submitted_at":"2015-04-04T02:14:48Z","abstract_excerpt":"Let $ (M,g) $ be a smooth compact Riemannian manifold of dimension $ N \\geq 3 $. Given $p_0 \\in M$, $\\lambda \\in \\mathcal{R}$ and $\\sigma \\in (0,2]$, we study existence and non existence of minimizers of the following quotient: \\begin{equation}\\label{Paper Equation} \\mu_{\\lambda,\\sigma}=\\inf_{u \\in H^1(M)\\setminus \\lbrace0\\rbrace} \\frac{\\displaystyle\\int_M |\\nabla u|^2 dv_g -\\lambda \\int_M u^2 dv_g }{\\biggl(\\displaystyle\\int_M \\rho^{-\\sigma} |u|^{2^*(\\sigma)} dv_g\\biggl)^{2/2^*(\\sigma)}}, \\end{equation} where $\\rho(.):=dist(p_0,.)$ denoted the geodesic distance from $p \\in M$ to $p_0$. In part"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00968","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"}