{"paper":{"title":"Sharp Regularity for the Integrability of Elliptic Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.CV","authors_text":"Brian Street","submitted_at":"2018-10-23T19:09:00Z","abstract_excerpt":"As part of his celebrated Complex Frobenius Theorem, Nirenberg showed that given a smooth elliptic structure (on a smooth manifold), the manifold is locally diffeomorphic to an open subset of $\\mathbb{R}^r\\times \\mathbb{C}^n$ (for some $r$ and $n$) in such a way that the structure is locally the span of $\\frac{\\partial}{\\partial t_1},\\ldots, \\frac{\\partial}{\\partial t_r},\\frac{\\partial}{\\partial \\overline{z}_1},\\ldots, \\frac{\\partial}{\\partial \\overline{z}_n}$; where $\\mathbb{R}^r\\times \\mathbb{C}^n$ has coordinates $(t_1,\\ldots, t_r, z_1,\\ldots, z_n)$. In this paper, we give optimal regularit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10057","kind":"arxiv","version":3},"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"}