{"paper":{"title":"Hearing pseudoconvexity in Lipschitz domains with holes via $\\overline\\partial$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Christine Laurent-Thi\\'ebaut, Mei-Chi Shaw, Siqi Fu","submitted_at":"2016-09-23T18:24:54Z","abstract_excerpt":"Let $\\Omega=\\widetilde{\\Omega}\\setminus \\overline{D}$ where $\\widetilde{\\Omega}$ is a bounded domain with connected complement in $\\mathbb C^n$ (or more generally in a Stein manifold) and $D$ is relatively compact open subset of $\\widetilde{\\Omega}$ with connected complement in $\\widetilde{\\Omega}$. We obtain characterizations of pseudoconvexity of $\\widetilde{\\Omega}$ and $D$ through the vanishing or Hausdorff property of the Dolbeault cohomology groups on various function spaces. In particular, we show that if the boundaries of $\\widetilde{\\Omega}$ and $D$ are Lipschitz and $C^2$-smooth resp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07454","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"}