{"paper":{"title":"A compactness theorem of the fractional Yamabe problem, Part I: The non-umbilic conformal infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Monica Musso, Seunghyeok Kim","submitted_at":"2018-08-15T02:35:51Z","abstract_excerpt":"Assume that $(X, g^+)$ is an asymptotically hyperbolic manifold, $(M, [\\bar{h}])$ is its conformal infinity, $\\rho$ is the geodesic boundary defining function associated to $\\bar{h}$ and $\\bar{g} = \\rho^2 g^+$. For any $\\gamma \\in (0,1)$, we prove that the solution set of the $\\gamma$-Yamabe problem on $M$ is compact in $C^2(M)$ provided that convergence of the scalar curvature $R[g^+]$ of $(X, g^+)$ to $-n(n+1)$ is sufficiently fast as $\\rho$ tends to 0 and the second fundamental form on $M$ never vanishes. Since most of the arguments in blow-up analysis performed here is irrelevant to the ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04951","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":""},"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"}