{"paper":{"title":"Existence of Complete conformal metrics of negative Ricci curvature on manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jeffrey Streets, Matthew Gursky, Micah Warren","submitted_at":"2009-07-27T14:32:12Z","abstract_excerpt":"We show that on a compact Riemannian manifold with boundary there exists $u \\in C^{\\infty}(M)$ such that, $u_{|\\partial M} \\equiv 0$ and $u$ solves the $\\sigma_k$-Ricci problem. In the case $k = n$ the metric has negative Ricci curvature. Furthermore, we show the existence of a complete conformally related metric on the interior solving the $\\sigma_k$-Ricci problem. By adopting results of Mazzeo-Pacard, we show an interesting relationship between the complete metrics we construct and the existence of Poincar\\'e-Einstein metrics. Finally we give a brief discussion of the corresponding questions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4641","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"}