{"paper":{"title":"Towering phenomena for the Yamabe equation on symmetric manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Filippo Morabito, Giusi Vaira","submitted_at":"2016-03-04T17:08:46Z","abstract_excerpt":"Let $(M,g)$ be a compact smooth connected Riemannian manifold (without boundary) of dimension $N\\ge7$. Assume $M$ is symmetric with respect to a point $\\xi_0$ with non-vanishing Weyl's tensor. We consider the linear perturbation of the Yamabe problem $$(P_\\epsilon)\\qquad-\\mathcal L_g u+\\epsilon u=u^{N+2\\over N-2}\\ \\hbox{in}\\ (M,g) .$$ We prove that for any $k\\in \\mathbb N$, there exists $\\epsilon_k>0$ such that for all $\\epsilon\\in (0, \\epsilon_k)$ the problem $(P_\\epsilon)$ has a symmetric solution $u_\\epsilon ,$ which looks like the superposition of $k$ positive bubbles centered at the point"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01538","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"}