{"paper":{"title":"Eigenvalue Estimate for the basic Laplacian on manifolds with foliated boundary, part II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Fida EL Chami, George Habib, Ola Makhoul, Roger Nakad","submitted_at":"2016-04-08T11:02:58Z","abstract_excerpt":"In [4], we gave a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic $1$-forms defined on a compact manifold whose boundary is endowed with a Riemannian flow. In this paper, we extend this result to the case of the first eigenvalue on basic $p$-forms for $p>1$. As in [4], the limiting case allows to characterize the manifold $\\mathbb{R} \\times B' / \\Gamma$ for some group $\\Gamma$, and where $B'$ denotes the unit closed ball. In particular, we describe the Riemannian product $\\mathbb{S}^1\\times \\mathbb{S}^n$ as the boundary of a manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02304","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"}