{"paper":{"title":"L^2 Harmonic 1-forms on submanifolds with finite total curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Feliciano Vitorio, Heudson Mirandola, Marcos P. Cavalcante","submitted_at":"2012-01-25T21:08:47Z","abstract_excerpt":"Let $x:M^m\\to \\bar M$, with $m\\geq 3$, be an isometric immersion of a complete noncompact manifold $M$ in a complete simply-connected manifold $\\bar M$ with sectional curvature satisfying $-c^2\\leq K_{\\bar M}\\leq 0$, for some constant $c$. Assume that the immersion has finite total curvature. If $c\\neq 0$, assume further that the first eigenvalue of the Laplacian of $M$ is bounded from below by a suitable constant. We prove that the space of the $L^2$ harmonic 1-forms on $M$ has finite dimension. Moreover there exists a constant $\\La>0$, explicitly computed, such that if the total curvature is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5392","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"}