{"paper":{"title":"Second Yamabe Constant on Riemannian Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guillermo Henry","submitted_at":"2015-05-05T12:27:54Z","abstract_excerpt":"Let $(M^m,g)$ be a closed Riemannian manifold $(m\\geq 2)$ of positive scalar curvature and $(N^n,h)$ any closed manifold. We study the asymptotic behaviour of the second Yamabe constant and the second $N-$Yamabe constant of $(M\\times N,g+th)$ as $t$ goes to $+\\infty$. We obtain that $\\lim_{t \\to +\\infty}Y^2(M\\times N,[g+th])=2^{\\frac{2}{m+n}}Y(M\\times \\re^n, [g+g_e]).$ If $n\\geq 2$, we show the existence of nodal solutions of the Yamabe equation on $(M\\times N,g+th)$ (provided $t$ large enough). When the scalar curvature of $(M,g)$ is constant, we prove that $\\lim_{t \\to +\\infty}Y^2_N(M\\times "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00981","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"}