{"paper":{"title":"Sharp quantitative stability of Struwe's decomposition of the Poincar\\'e-Sobolev inequalities on the hyperbolic space: Part I","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Debabrata Karmakar, Debdip Ganguly, Mousomi Bhakta, Saikat Mazumdar","submitted_at":"2022-11-26T17:13:11Z","abstract_excerpt":"A classical result owing to Mancini and Sandeep [Ann. Sc. Norm. Super. Pisa Cl. Sci. 7 (2008)] asserts that all positive solutions of the Poincar\\'e-Sobolev equation on the hyperbolic space $$ -\\Delta_{\\mathbb{B}^n} u-\\lambda u = |u|^{p-1}u, \\quad u\\in H^1(\\mathbb{B}^n), $$ are unique up to hyperbolic isometries where $n \\geq 3,$ $1 < p \\leq \\frac{n+2}{n-2} $ and $\\lambda \\leq \\frac{(n-1)^2}{4}.$ We prove under certain bounds on $\\|\\nabla u \\|_{L^2(\\mathbb{B}^n)}$ the inequality $$ \\delta(u) \\lesssim \\|\\Delta_{\\mathbb{B}^n} u+ \\lambda u + u^{p}\\|_{H^{-1}}, $$\n  holds whenever $p >2$ and hence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.14618","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.14618/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"}