{"paper":{"title":"Flowing to free boundary minimal surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Christopher Wright, Melanie Rupflin, Michael Struwe","submitted_at":"2026-05-19T09:19:11Z","abstract_excerpt":"We introduce a flow that is designed to flow maps $u:\\Sigma\\to \\mathbb{R}^n$ which map the boundary of a general domain surface $\\Sigma$ into a given (not necessarily connected) submanifold $N\\hookrightarrow \\mathbb{R}^n$ towards a free boundary (branched) minimal immersion supported by $N$. In the case when $\\Sigma$ is the unit disc $D$, this task can be achieved by means of the Plateau-flow introduced in the work [15] of the second author. When $\\Sigma\\neq D$, however, also the conformal type of the domain metric plays a role and it no longer suffices to deform the trace of the given map int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19574","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.19574/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"}