{"paper":{"title":"Free boundary minimal surfaces in the unit 3-ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Abigail Folha, Frank Pacard (CMLS-EcolePolytechnique), Tatiana Zolotareva (CMLS-EcolePolytechnique)","submitted_at":"2015-02-24T13:50:37Z","abstract_excerpt":"In a recent paper A. Fraser and R. Schoen have proved the existence of free boundary minimal surfaces $\\Sigma\\_n$ in $B^3$ which have genus $0$ and $n$ boundary components, for all $ n \\geq 3$. For large $n$, we give an independent construction of $\\Sigma\\_n$ and prove the existence of free boundary minimal surfaces $\\tilde \\Sigma\\_n$ in $B^3$ which have genus $1$ and $n$ boundary components. As $n$ tends to infinity, the sequence $\\Sigma\\_n$ converges to a double copy of the unit horizontal (open) disk, uniformly on compacts of $B^3$ while the sequence $\\tilde \\Sigma\\_n$ converges to a double"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06812","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"}