{"paper":{"title":"A non-compactness result on the fractional Yamabe problem in large dimensions","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":"2015-05-22T19:18:34Z","abstract_excerpt":"Let $(X^{n+1}, g^+)$ be an $(n+1)$-dimensional asymptotically hyperbolic manifold with a conformal infinity $(M^n, [\\hat{h}])$. The fractional Yamabe problem addresses to solve \\[P^{\\gamma}[g^+,\\hat{h}] (u) = cu^{n+2\\gamma \\over n-2\\gamma}, \\quad u > 0 \\quad \\text{on } M\\] where $c \\in \\mathbb{R}$ and $P^{\\gamma}[g^+,\\hat{h}]$ is the fractional conformal Laplacian whose principal symbol is $(-\\Delta)^{\\gamma}$. In this paper, we construct a metric on the half space $X = \\mathbb{R}^{n+1}_+$, which is conformally equivalent to the unit ball, for which the solution set of the fractional Yamabe eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06183","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"}