{"paper":{"title":"On the $L^2$-Dolbeault cohomology of annuli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Christine Laurent-Thi\\'ebaut, Debraj Chakrabarti, Mei-Chi Shaw","submitted_at":"2016-02-11T21:04:30Z","abstract_excerpt":"For certain annuli in $\\mathbb{C}^n$, $n\\geq 2$, with non-smooth holes, we show that the $\\bar{\\partial}$-operator from $L^2$ functions to $L^2$ $(0,1)$-forms has closed range. The holes admitted include products of pseudoconvex domains and certain intersections of smoothly bounded pseudoconvex domains. As a consequence, we obtain estimates in the Sobolev space $W^1$ for the $\\bar{\\partial}$-equation on the non-smooth domains which are the holes of these annuli."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03896","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"}