{"paper":{"title":"Quantitative stability of critical points for the nonlocal-Sobolev inequality in Heisenberg group","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jialin Wang, Jijie Xu, Shuijin Zhang","submitted_at":"2025-08-12T03:54:23Z","abstract_excerpt":"We investigate the quantitative stability of the nonlocal Sobolev inequality in Heisenberg group \\begin{equation*}\\label{non-Sobolev}\n  C_{HL}(Q,\\mu) \\left(\\int_{\\mathbb{H}^{n}}\\int_{\\mathbb{H}^{n}}\\frac{|u(\\xi)|^{Q^{\\ast}_{\\mu}}|u(\\eta)|^{Q^{\\ast}_{\\mu}}}{|\\eta^{-1}\\xi|^{\\mu}}\\mathrm{d}\\xi\\mathrm{d}\\eta\\right)^{\\frac{1}{Q^{\\ast}_{\\mu}}}\\leq \\int_{\\mathbb{H}^{n}}|\\nabla_{H}u|^{2}d\\xi,\\qquad\\forall u\\in S^{1,2}(\\mathbb{H}^{n}), \\end{equation*} where $Q=2n+2$ is the homogeneous dimension of the Hiesenberg group $\\mathbb{H}^{n}$, $\\mu\\in(0,Q)$ and $Q^{\\ast}_{\\mu}=\\frac{2Q-\\mu}{Q-2}$ are two param"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.08614","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/2508.08614/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"}