{"paper":{"title":"Some remarks on singular capillary cones with free boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alberto Pacati, Bozhidar Velichkov, Giorgio Tortone","submitted_at":"2025-02-11T16:50:40Z","abstract_excerpt":"We study minimizing singular cones with free boundary associated with the capillarity problem. Precisely, we provide a stability criterion $\\`a$ la Jerison-Savin for capillary hypersurfaces and show that, in dimensions up to $4$, minimizing cones with non-sign-changing mean curvature are flat. We apply this criterion to minimizing capillary drops and, additionally, establish the instability of non-trivial axially symmetric cones in dimensions up to $6$.\n  The main results are based on a Simons-type inequality for a class of convex, homogeneous, symmetric functions of the principal curvatures, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07697","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/2502.07697/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"}