{"paper":{"title":"Clustering phenomena for linear perturbation of the Yamabe equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Giusi Vaira","submitted_at":"2015-11-22T16:19:59Z","abstract_excerpt":"Let $(M,g)$ be a non-locally conformally flat compact Riemannian manifold with dimension $N\\ge7.$ We are interested in finding positive solutions to the linear perturbation of the Yamabe problem $$-\\mathcal L_g u+\\epsilon u=u^{N+2\\over N-2}\\ \\hbox{in}\\ (M,g) $$ where the first eigenvalue of the conformal laplacian $-\\mathcal L_g $ is positive and $\\epsilon$ is a small positive parameter. We prove that for any point $\\xi_0\\in M$ which is non-degenerate and non-vanishing minimum point of the Weyl's tensor and for any integer $k$ there exists a family of solutions developing $k$ peaks collapsing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07028","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"}