{"paper":{"title":"On the rigidity of manifolds with respect to Gagliardo-Nirenberg inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Liang Cheng","submitted_at":"2025-07-08T11:51:10Z","abstract_excerpt":"In this paper, we investigate local rigidity properties related to Gagliardo-Nirenberg constants and unweighted Yamabe-type constants. Let $V$ be an open bounded subset of an $n$-dimensional Riemannian manifold $(M,g)$ whose Gagliardo-Nirenberg constant satisfies\n  \\[\n  \\mathbb{G}_{\\alpha}^{\\pm}(V,g) \\geq \\mathbb{G}_{\\alpha}^{\\pm}(\\mathbb{R}^n,g_{\\mathbb{R}^n}),\n  \\]\n  where $(\\mathbb{R}^n,g_{\\mathbb{R}^n})$ denotes the $n$-dimensional Euclidean space with its standard metric. We show that for $\\alpha \\in (0,1) \\cup \\left(1,\\frac{n+6}{n+2}\\right)$ when $n \\leq 6$ or $\\alpha \\in (0,1) \\cup \\lef"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05908","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/2507.05908/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"}