{"paper":{"title":"Regularity of minimal surfaces with capillary boundary conditions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Carlo Gasparetto, Chao Li, Luigi De Masi, Nick Edelen","submitted_at":"2024-05-31T13:57:57Z","abstract_excerpt":"We prove $\\varepsilon$-regularity theorems for varifolds with capillary boundary condition in a Riemannian manifold. These varifolds were first introduced by Kagaya-Tonegawa \\cite{KaTo}. We establish a uniform first variation control for all such varifolds (and free-boundary varifolds generally) satisfying a sharp density bound and prove that if a capillary varifold has bounded mean curvature and is close to a capillary half-plane with angle not equal to $\\tfrac{\\pi}{2}$, then it coincides with a $C^{1,\\alpha}$ properly embedded hypersurface. We apply our theorem to deduce regularity at a gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.20796","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/2405.20796/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"}