{"paper":{"title":"Allard's interior $\\varepsilon$-Regularity Theorem in Alexandrov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MG"],"primary_cat":"math.DG","authors_text":"Julio C. Correa Hoyos, M\\'arcio Fabiano da Silva, Marcos Agnoletto, Stefano Nardulli","submitted_at":"2025-04-14T23:18:09Z","abstract_excerpt":"In this paper, we prove Allard's Interior $\\varepsilon$-Regularity Theorem for $m$-dimensional varifolds with generalized mean curvature in $L^p_{loc}$, $p > m$, in non-collapsed Alexandrov spaces with curvature bounded both from above and below. We first develop an intrinsic proof of the theorem for varifolds in Riemannian manifolds with metric tensor of class $\\mathcal{C}^2$, without appealing to Nash's Isometric Embedding Theorem. This yields explicitly computable constants depending only on $m$, $n$, the double sided sectional curvature bounds, and the harmonic radius (or, equivalently, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.10758","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/2504.10758/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"}