{"paper":{"title":"Scalar Curvature Flexibility in the Riemannian Burnett Compactness Class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jingbo Wan","submitted_at":"2026-08-09T13:39:46Z","abstract_excerpt":"Let $M$ be a connected smooth $n$-manifold without boundary, where $n\\geq3$, and let $\\kappa\\in\\mathbb{R}$, with $\\kappa\\leq0$ if $M$ is open. We prove that every smooth Riemannian metric $g_0$ with $\\mathrm{Scal}_{g_0}\\geq\\kappa$ is a locally uniform limit of smooth Riemannian metrics $g_i$ with $\\mathrm{Scal}_{g_i}=\\kappa$ that are locally uniformly bounded in $W^{1,\\infty}$. As a corollary, combining this with Gromov's $C^0$-stability theorem, we obtain the perhaps surprising identity \\[ \\overline{\\{g:\\mathrm{Scal}_g=\\kappa\\}}^{\\,C^{0,\\alpha}_{\\mathrm{loc}}}=\\{g:\\mathrm{Scal}_g\\geq\\kappa\\},"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08707","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/2608.08707/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"}