{"paper":{"title":"The number of minimal surfaces bounded by Enneper's wire","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Michael Beeson","submitted_at":"2015-05-22T19:08:07Z","abstract_excerpt":"Enneper's wire, the image of the circle of radius $R$ under Enneper's surface, bounds exactly three minimal surfaces for $R$ between 1 and $\\sqrt 3$, and these three surfaces depend continuously on $R$.\n  The other two surfaces (besides Enneper's surface) are absolute minima of area among disk-type surfaces bounded by Enneper's wire. These surfaces each have a unique horizontal tangent plane, whose height can be computed from $R$, and they are invariant under reflections in the planes $x_1=0$ and $x_2 = 0$. These two surfaces have positive second variation of area, and depend continuously on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03064","kind":"arxiv","version":4},"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"}