{"paper":{"title":"Optimal Stability Bounds, Minimizers, and Critical Points for a Critical Nonlocal Sobolev Inequality on the Heisenberg Group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenjing Chen, Zexi Wang","submitted_at":"2026-08-10T02:36:40Z","abstract_excerpt":"We investigate the optimal Bianchi-Egnell-type quantitative stability constant for the critical nonlocal Sobolev inequality on the Heisenberg group $\\mathbb{H}^{n}$, \\begin{equation}\\label{nS}\n  S_{HL}(Q,\\mu)\\left(\\int_{\\mathbb{H}^{n}}\\int_{\\mathbb{H}^{n}}\n  \\frac{|u(\\xi)|^{Q^{\\ast}_{\\mu}}|u(\\eta)|^{Q^{\\ast}_{\\mu}}}\n  {|\\eta^{-1}\\xi|^{\\mu}}\\,d\\xi d\\eta\\right)^{\\frac{1}{Q^{\\ast}_{\\mu}}}\n  \\leq \\int_{\\mathbb{H}^{n}}|\\nabla_{\\mathbb{H}}u|^{2}d\\xi,\n  \\qquad u\\in S^{1,2}(\\mathbb{H}^{n}), \\end{equation} where $Q=2n+2$, $n\\geq1$, $0<\\mu<Q$, and $Q^{\\ast}_{\\mu}=(2Q-\\mu)/(Q-2)$. Let $\\mathfrak{M}$ deno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09034","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/2608.09034/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"}