{"paper":{"title":"An implicit function theorem for Lipschitz mappings into metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.GT","authors_text":"Piotr Haj{\\l}asz, Scott Zimmerman","submitted_at":"2018-09-18T16:57:56Z","abstract_excerpt":"We prove a version of the implicit function theorem for Lipschitz mappings $f:\\mathbb{R}^{n+m}\\supset A \\to X$ into arbitrary metric spaces. As long as the pull-back of the Hausdorff content $\\mathcal{H}_{\\infty}^n$ by $f$ has positive upper $n$-density on a set of positive Lebesgue measure, then, there is a local diffeomorphism $G$ in $\\mathbb{R}^{n+m}$ and a Lipschitz map $\\pi:X\\to \\mathbb{R}^n$ such that $\\pi\\circ f\\circ G^{-1}$, when restricted to a certain subset of $A$ of positive measure, is a the orthogonal projection of $\\mathbb{R}^{n+m}$ onto the first $n$-coordinates. This may be se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06829","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"}