{"paper":{"title":"On the boundary behavior of mass-minimizing integral currents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Annalisa Massaccesi, Camillo De Lellis, Guido De Philippis, Jonas Hirsch","submitted_at":"2018-09-25T13:19:18Z","abstract_excerpt":"Let $\\Sigma$ be a smooth Riemannian manifold, $\\Gamma \\subset \\Sigma$ a smooth closed oriented submanifold of codimension higher than $2$ and $T$ an integral area-minimizing current in $\\Sigma$ which bounds $\\Gamma$. We prove that the set of regular points of $T$ at the boundary is dense in $\\Gamma$. Prior to our theorem the existence of any regular point was not known, except for some special choice of $\\Sigma$ and $\\Gamma$. As a corollary we answer to a question of Almgren about the connectivity of minimizers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09457","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1809.09457/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}