{"paper":{"title":"The Dirichlet problem for the minimal surface equation on unbounded helicoidal domains of $\\mathbb{R}^{m}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Ari Aiolfi, Caroline Assmann, Jaime Ripoll","submitted_at":"2023-06-17T17:03:26Z","abstract_excerpt":"We consider a helicoidal group $G$ in $\\mathbb{R}^{n+1}$ and unbounded $G$-invariant $C^{2,\\alpha}$-domains $\\Omega\\subset\\mathbb{R}^{n+1}$ whose helicoidal projections are exterior domains in $\\mathbb{R}^{n}$, $n\\geq2$. We show that for all $s\\in\\mathbb{R}$, there exists a $G$-invariant solution $u_{s}\\in C^{2,\\alpha}\\left( \\overline{\\Omega}\\right) $ of the Dirichlet problem for the minimal surface equation with zero boundary data which satisfies $\\sup_{\\partial\\Omega}\\left\\vert \\operatorname{grad}u_{s}\\right\\vert =\\left\\vert s\\right\\vert $. Additionally, we provide further information on the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.10391","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.10391/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}