{"paper":{"title":"A Multiple-Valued Plateau Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Quentin Funk, Robert Hardt","submitted_at":"2015-07-07T17:52:12Z","abstract_excerpt":"The existence of Dirichlet minimizing multiple-valued functions for given boundary data has been known since pioneering work of F. Almgren. Here we prove a multiple-valued analogue of the classical Plateau problem of the existence of area-minimizing mappings of the disk. Specifically, we find, for $K \\in \\mathbb N,$ $k_1,...,k_K\\in \\mathbb N$ with sum $Q$ and any collection of $K$ disjoint Lipschitz Neighborhood Retract Jordan curves, optimal multiple-valued boundary data with these multiplicities which extends to a Dirichlet minimizing $Q$-valued function with minimal Dirichlet energy among a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01896","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"}