{"paper":{"title":"Sharp quantitative stability of Poincare-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Debabrata Karmakar, Debdip Ganguly, Mousomi Bhakta, Saikat Mazumdar","submitted_at":"2022-07-22T11:57:08Z","abstract_excerpt":"Consider the Poincar\\'e-Sobolev inequality on the hyperbolic space: for every $n \\geq 3$ and $1 < p \\leq \\frac{n+2}{n-2},$ there exists a best constant $S_{n,p, \\lambda}(\\mathbb{B}^{n})>0$ such that $$S_{n, p, \\lambda}(\\mathbb{B}^{n})\\left(~\\int \\limits_{\\mathbb{B}^{n}}|u|^{{p+1}} \\, {\\rm d}v_{\\mathbb{B}^n} \\right)^{\\frac{2}{p+1}}\n  \\leq\\int \\limits_{\\mathbb{B}^{n}}\\left(|\\nabla_{\\mathbb{B}^{n}}u|^{2}-\\lambda u^{2}\\right) \\, {\\rm d}v_{\\mathbb{B}^n},$$ holds for all $u\\in C_c^{\\infty}(\\mathbb{B}^n),$ and $\\lambda \\leq \\frac{(n-1)^2}{4},$ where $\\frac{(n-1)^2}{4}$ is the bottom of the $L^2$-spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.11024","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.11024/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}