{"paper":{"title":"Regularity of minimal hypersurfaces with a common free boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Brian Krummel","submitted_at":"2013-09-24T16:37:10Z","abstract_excerpt":"Let $N$ be a Riemannian manifold and consider a stationary union of three or more $C^{1,\\mu}$ hypersurfaces-with-boundary $M_k$ in $N$ with a common boundary $\\Gamma$. We show that if $N$ is smooth, then $\\Gamma$ is smooth and each $M_k$ is smooth up to $\\Gamma$ (real analytic in the case $N$ is real analytic). Consequently we strengthen a result of Wickramasekera to conclude that under the stronger hypothesis that $V$ is a stationary, stable, integral $n$-varifold in an $(n+1)$-dimensional, smooth (real analytic) Riemannian manifold such that the support of $\\|V\\|$ is nowhere locally the unio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6245","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"}