{"paper":{"title":"Global Regularity for the Tangential Cauchy-Riemann Operator on Weakly Pseudoconvex CR Manifolds","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Andreea Nicoara","submitted_at":"2005-12-03T02:26:44Z","abstract_excerpt":"Let M of real dimension 2n-1 be a compact, orientable, weakly pseudoconvex manifold of dimension at least five, embedded in C^N (n less than or equal to N), of codimension one or more in C^N, and endowed with the induced CR structure. We show the tangential Cauchy-Riemann operator has closed range on such a manifold M, hence we get global existence and regularity results for the \\bar\\partial_b problem. We also show the middle (i.e. corresponding to (p,q) forms for q between 1 and n-2) \\bar\\partial_b cohomology groups of M with respect to L^2, Sobolev s, and smooth coefficients are finite and i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512072","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"}