{"paper":{"title":"On the volume functional of compact manifolds with boundary with harmonic Weyl tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"H. Baltazar, K. Bezerra, R. Batista","submitted_at":"2017-10-17T13:03:25Z","abstract_excerpt":"One of the main aims of this article is to give the complete classification of critical metrics of the volume functional on a compact manifold $M$ with boundary $\\partial M$ and with harmonic Weyl tensor, which improves the corresponding classification for complete locally conformally flat case, due to Miao and Tam [18]. In particular, we prove that a critical metric with harmonic Weyl tensor on a simply connected compact manifold with boundary isometric to a standard sphere $\\mathbb{S}^{n-1}$ must be isometric to a geodesic ball in a simply connected space form $\\Bbb{R}^n,$ $\\Bbb{H}^n$ and $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06247","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"}