{"paper":{"title":"On the sharp constants in curl-Sobolev inequalities on $\\mathbb{S}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.DG","authors_text":"Guofang Wang, Mingwei Zhang","submitted_at":"2026-07-21T13:30:26Z","abstract_excerpt":"Let $n\\equiv 3\\ (\\mathrm{mod}\\ 4)$ and set $p=\\frac{n-1}{2}$. On an oriented Riemannian $n$-manifold we consider the (middle-degree) curl operator, $\\mathrm{curl}:*\\mathrm{d}:\\Omega^{p}\\rightarrow\\Omega^{p}$, and the associated conformally invariant Sobolev quotients on $(\\mathbb{S}^n,g_{\\mathrm{st}})$, \\[ J_1(\\alpha)=\\frac{\\big(\\int|\\mathrm{curl}\\alpha|^{\\frac{2n}{n+1}}\\,\\mathrm{dV}\\big)^{\\frac{n+1}{n}}}{\\int\\langle\\mathrm{curl}\\alpha,\\alpha\\rangle\\,\\mathrm{dV}}, \\qquad J_2(\\alpha)=\\frac{\\big(\\int|\\mathrm{curl}\\alpha|^{\\frac{2n}{n+1}}\\,\\mathrm{dV}\\big)^{\\frac{n+1}{n}}}{\\inf_{\\phi}\\big(\\int|\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19091","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/2607.19091/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"}