{"paper":{"title":"Sharp quantitative stability of the Yamabe problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haixia Chen, Seunghyeok Kim","submitted_at":"2024-04-22T08:08:07Z","abstract_excerpt":"Given a smooth closed Riemannian manifold $(M,g)$ of dimension $N \\ge 3$, we derive sharp quantitative stability estimates for nonnegative functions near the solution set of the Yamabe problem on $(M,g)$. The seminal work of Struwe (1984) \\cite{S} states that if $\\Gamma(u) := \\|\\Delta_g u - \\frac{N-2}{4(N-1)} R_g u + u^{\\frac{N+2}{N-2}}\\|_{H^{-1}(M)} \\to 0$, then $\\|u-(u_0+\\sum_{i=1}^{\\nu} \\mathcal{V}_i)\\|_{H^1(M)} \\to 0$ where $u_0$ is a solution to the Yamabe problem on $(M,g)$, $\\nu \\in \\mathbb{N} \\cup \\{0\\}$, and $\\mathcal{V}_i$ is a bubble-like function. If $M$ is the round sphere $\\mathb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.13961","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/2404.13961/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"}