{"paper":{"title":"Minimal immersions of compact bordered Riemann surfaces with free boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ailana Fraser, Chao Pang, Jingyi Chen","submitted_at":"2012-09-06T03:00:25Z","abstract_excerpt":"Let N be a complete, homogeneously regular Riemannian manifold of dimension greater than 2 and let M be a compact submanifold of N. Let $\\Sigma$ be a compact orientable surface with boundary. We show that for any continuous $f: (\\Sigma, \\partial \\Sigma) \\rightarrow (N, M)$ for which the induced homomorphism on certain fundamental groups is injective, there exists a branched minimal immersion of $\\Sigma$ solving the free boundary problem $(\\Sigma, \\partial \\Sigma) \\rightarrow (N, M)$, and minimizing area among all maps which induce the same action on the fundamental groups as f. Furthermore, un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1165","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"}