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We prove the existence of a solution to the supercritical problems $$ -\\Delta_gu+\\kappa u= u^p,\\ u>0\\quad\\hbox{in}\\ (M,g)\\quad\\hbox{and}\\quad-\\Delta_gu+\\kappa u=\\lambda e^u\\quad\\hbox{in}\\ (M,g) $$ which concentrate s along a $(m-1)-$dimensional submanifold of $M$ as $p\\to\\infty$ and $\\lambda\\to0$, respectively, under suitable symmetry assumptions on the manifold $M$."},"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":"1309.2661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-10T20:29:44Z","cross_cats_sorted":[],"title_canon_sha256":"60dd2dbe1d89b884d8fc46a8097a27ed1b4c87c4c471fc0db26b0b922a0fb7bd","abstract_canon_sha256":"c48d3f30f1a8314225ad8098a79ef31128b287d26265e1dc661fcc18c518f78c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:35.288099Z","signature_b64":"Hg/09PNkYZWW4fcIQeOJzRG5p+0RgGrEjNaB5rRtTerhUcs30raLz8LMsjh1xBUFNEX50GF9UkfuCJxWPzqSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f489d6b6d97ed67204d5d6d41398784f50620d21d7138b7e040478780433db7a","last_reissued_at":"2026-05-18T03:13:35.287467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:35.287467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Supercritical problems on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Giusi Vaira","submitted_at":"2013-09-10T20:29:44Z","abstract_excerpt":"Let $(M,g)$ be a $m$-dimensional compact Riemannian manifold without boundary. Assume $\\kappa\\in C^2(M)$ is such that $-\\Delta_g+\\kappa$ is coercive. 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