{"paper":{"title":"On the asymptotic behavior of Einstein manifolds with an integral bound on the Weyl curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.AP"],"primary_cat":"math.DG","authors_text":"Dandan Ji, Romain Gicquaud, Yuguang Shi","submitted_at":"2012-10-03T06:48:23Z","abstract_excerpt":"In this paper we consider the geometric behavior near infinity of some Einstein manifolds $(X^n, g)$ with Weyl curvature belonging to a certain $L^p$ space. Namely, we show that if $(X^n, g)$, $n \\geq 7$, admits an essential set and has its Weyl curvature in $L^p$ for some $1<p<\\frac{n-1}{2}$, then $(X^n, g)$ must be asymptotically locally hyperbolic. One interesting application of this theorem is to show a rigidity result for the hyperbolic space under an integral condition for the curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1005","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":""},"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"}