{"paper":{"title":"Free boundary minimal surfaces of unbounded genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Daniel Ketover","submitted_at":"2016-12-27T18:01:28Z","abstract_excerpt":"For each integer $g\\geq 1$ we use variational methods to construct in the unit $3$-ball $B$ a free boundary minimal surface $\\Sigma_g$ of symmetry group $\\mathbb{D}_{g+1}$. For $g$ large, $\\Sigma_g$ has three boundary components and genus $g$. As $g\\rightarrow\\infty$ the surfaces $\\Sigma_g$ converge as varifolds to the union of the disk and critical catenoid. These examples are the first with genus greater than $1$ and were conjectured to exist by Fraser-Schoen. We also construct several new free boundary minimal surfaces in $B$ with the symmetry groups of the cube, tetrahedron and dodecahedro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08691","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":""},"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"}