{"paper":{"title":"Generic finiteness of minimal surfaces with bounded Morse index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alessandro Carlotto","submitted_at":"2015-09-23T19:23:45Z","abstract_excerpt":"Given a compact 3-manifold N without boundary, we prove that for a bumpy metric of positive scalar curvature the space of minimal surfaces having a uniform upper bound on the Morse index is always finite unless the manifold itself contains an embedded minimal RP^2. In particular, we derive a generic finiteness result whenever N does not contain a copy of RP^3 in its prime decomposition. We discuss the obstructions to any further generalization of such a result. When the metric g is required to be (scalar positive and) strongly bumpy (meaning that all closed, immersed minimal surfaces do not ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07101","kind":"arxiv","version":4},"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"}