{"paper":{"title":"Stability of spinorial Sobolev inequalities on $\\mathbb{S}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.DG","authors_text":"Guofang Wang, Mingwei Zhang","submitted_at":"2025-08-12T16:09:08Z","abstract_excerpt":"The spinorial Sobolev inequality on the unit sphere states \\begin{equation*}\n  \\Big(\\int| D\\psi|^{\\frac{2n}{n+1}}\\Big)^{\\frac{n+1}{n}}-\\frac{n}{2}\\omega_{n}^{1/n}\\int\\langle D\\psi,\\psi\\rangle\n  \\geq 0, \\end{equation*} with equality if and only if $\\psi \\in {\\mathcal M}$, the set of all $-\\frac 12$-Killing spinors and their conformal transformations.\n  Our main result in this paper is to refine this inequality by establishing a stability inequality\n  \\begin{equation*} \\Big(\\int| D\\psi|^{\\frac{2n}{n+1}}\\Big)^{\\frac{n+1}{n}}-\\frac{n}{2}\\omega_{n}^{1/n}\\int\\langle D\\psi,\\psi\\rangle\n  \\geq {\\bf c}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.09047","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/2508.09047/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"}