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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.00981","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-05T12:27:54Z","cross_cats_sorted":[],"title_canon_sha256":"26ccc13d88305d7bfd253abe60db69919f9e26a4f459a564b8272eddeb30a53b","abstract_canon_sha256":"53416cd9b8979d74b01dfdaa068cc7e51d7727464870706c12c30c7ceb9d9b13"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:06.598487Z","signature_b64":"SuZ4FBRCCHONgVpKZWKyITM07hDWcrz0eDXm9vkPRMQPyu/3VHCJKqMOAHkdgB6ThfWFIqZ3RU+VO2aroSZ3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2a67cf5cd559eb1db35897d37f124fbcdd1416c86263dc23ada8b4af2db1cef","last_reissued_at":"2026-05-18T00:56:06.597958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:06.597958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.00981","created_at":"2026-05-18T00:56:06.598034+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.00981v2","created_at":"2026-05-18T00:56:06.598034+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00981","created_at":"2026-05-18T00:56:06.598034+00:00"},{"alias_kind":"pith_short_12","alias_value":"YKTHZ5ONKWPL","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"YKTHZ5ONKWPLDWZV","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"YKTHZ5ON","created_at":"2026-05-18T12:29:50.041715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YKTHZ5ONKWPLDWZVRF6TP4JE7P","json":"https://pith.science/pith/YKTHZ5ONKWPLDWZVRF6TP4JE7P.json","graph_json":"https://pith.science/api/pith-number/YKTHZ5ONKWPLDWZVRF6TP4JE7P/graph.json","events_json":"https://pith.science/api/pith-number/YKTHZ5ONKWPLDWZVRF6TP4JE7P/events.json","paper":"https://pith.science/paper/YKTHZ5ON"},"agent_actions":{"view_html":"https://pith.science/pith/YKTHZ5ONKWPLDWZVRF6TP4JE7P","download_json":"https://pith.science/pith/YKTHZ5ONKWPLDWZVRF6TP4JE7P.json","view_paper":"https://pith.science/paper/YKTHZ5ON","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.00981&json=true","fetch_graph":"https://pith.science/api/pith-number/YKTHZ5ONKWPLDWZVRF6TP4JE7P/graph.json","fetch_events":"https://pith.science/api/pith-number/YKTHZ5ONKWPLDWZVRF6TP4JE7P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YKTHZ5ONKWPLDWZVRF6TP4JE7P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YKTHZ5ONKWPLDWZVRF6TP4JE7P/action/storage_attestation","attest_author":"https://pith.science/pith/YKTHZ5ONKWPLDWZVRF6TP4JE7P/action/author_attestation","sign_citation":"https://pith.science/pith/YKTHZ5ONKWPLDWZVRF6TP4JE7P/action/citation_signature","submit_replication":"https://pith.science/pith/YKTHZ5ONKWPLDWZVRF6TP4JE7P/action/replication_record"}},"created_at":"2026-05-18T00:56:06.598034+00:00","updated_at":"2026-05-18T00:56:06.598034+00:00"}