{"paper":{"title":"Bott-Chern Harmonic Forms on Stein Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Adriano Tomassini, Riccardo Piovani","submitted_at":"2018-06-04T07:09:43Z","abstract_excerpt":"Let $M$ be an $n$-dimensional $d$-bounded Stein manifold $M$, i.e., a complex $n$-dimensional manifold $M$ admitting a smooth strictly plurisubharmonic exhaustion $\\rho$ and endowed with the K\\\"ahler metric whose fundamental form is $\\omega=i\\partial\\overline{\\partial}\\rho$, such that $i\\overline{\\partial}\\rho$ has bounded $L^\\infty$ norm. We prove a vanishing result for $W^{1,2}$ harmonic forms with respect to the Bott-Chern Laplacian on $M$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00987","kind":"arxiv","version":1},"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"}