{"paper":{"title":"On free boundary minimal submanifolds in geodesic balls in $\\mathbb H^n$ and $\\mathbb S^n_+$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Vladimir Medvedev","submitted_at":"2023-11-04T14:09:55Z","abstract_excerpt":"We consider free boundary minimal submanifolds in geodesic balls in the hyperbolic space $\\mathbb H^n$ and in the round upper hemisphere $\\mathbb S^n_+$. Recently, Lima and Menezes have found a connection between free boundary minimal surfaces in geodesic balls in $\\mathbb S^n_+$ and maximal metrics for a functional, defined on the set of Riemannian metrics on a given compact surface with boundary. This connection is similar to the connection between free boundary minimal submanifolds in Euclidean balls and the critical metrics of the functional \"the $k$-th normalized Steklov eigenvalue\", intr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.02409","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/2311.02409/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"}