{"paper":{"title":"The \\bar\\partial_b Equation on Weakly Pseudoconvex CR Manifolds of Dimension 3","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Andreea Nicoara, Joseph J. Kohn","submitted_at":"2005-12-03T03:48:55Z","abstract_excerpt":"Let M be a smooth, compact, orientable, weakly pseudoconvex manifold of dimension 3, embedded in C^N (N greater than or equal to 2), of codimension one or more in C^N, and endowed with the induced CR structure. Assuming that the tangential Cauchy-Riemann operator \\bar\\partial_b has closed range in L^2 in order to rule out the Rossi example, we push regularity up to show \\bar\\partial_b has closed range in all Sobolev spaces s for s greater than zero. We then use the Szeg\\\"{o} projection to show there is a smooth solution to the \\bar\\partial_b problem given smooth data. The results are obtained "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512073","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"}