{"paper":{"title":"On the existence of foliations by solutions to the exterior Dirichlet problem for the minimal surface equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Ari Aiolfi, Daniel Bustos, Jaime Ripoll","submitted_at":"2020-12-27T19:33:30Z","abstract_excerpt":"Given an exterior domain $\\Omega$ with $C^{2,\\alpha}$ boundary in $\\mathbb{R}^{n}$, $n\\geq3$, we obtain a $1$-parameter family $u_{\\gamma}\\in C^{\\infty}\\left(\\Omega\\right) $, $\\left\\vert \\gamma\\right\\vert \\leq\\pi/2$, of solutions of the minimal surface equation such that, if $\\left\\vert \\gamma\\right\\vert <\\pi/2$, $u_{\\gamma}\\in C^{\\infty}\\left( \\Omega\\right) \\cap C^{2,\\alpha}\\left( \\overline{\\Omega}\\right) $, $u_{\\gamma}|_{\\partial\\Omega}=0$ with $\\max_{\\partial\\Omega}\\left\\Vert \\nabla u_{\\gamma}\\right\\Vert =\\tan\\gamma$ and, if $\\left\\vert \\gamma\\right\\vert =\\pi/2$, the graph of $u_{\\gamma}$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.14003","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.14003/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"}