{"paper":{"title":"A Local Minimizing Property of Strictly Stable Free Boundary Minimal Hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hangyue Zhu, Xiaoxiang Jiao","submitted_at":"2026-05-25T08:34:58Z","abstract_excerpt":"We prove a local minimizing property for strictly stable free-boundary minimal hypersurfaces in the relative current setting. Let $\\Sigma^n$ be a compact, two-sided, properly embedded free-boundary minimal hypersurface in a compact Riemannian manifold $(N^{n+1},\\partial N)$. If $\\Sigma$ is strictly stable, then, in a sufficiently small free-boundary adapted tubular neighborhood $K_r$, the relative cycle $\\llbracket\\Sigma\\rrbracket$ is the unique mass minimizer in its relative $\\mathbb Z_2$-homology class in $(K_r,K_r\\cap\\partial N)$.\n  We further prove a relative flat-neighborhood version, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25585","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/2605.25585/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"}