{"paper":{"title":"On free boundary minimal submanifolds with boundary on concentric spheres in Euclidean spac","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Tianyu Ma, Vladimir Medvedev","submitted_at":"2026-06-22T20:50:10Z","abstract_excerpt":"The search for free boundary minimal submanifolds in Euclidean space with boundaries on a collection of concentric spheres naturally extends the classical problem in the unit Euclidean ball. A key feature of this setting is that the coordinate functions of such submanifolds satisfy a Steklov problem with an indefinite weight. This framework allows us to introduce a spectral index, which in turn yields both upper and lower bounds for the Morse index. As a concrete application, we compute the exact Morse index of an $m$-dimensional flat annulus in an $n$-dimensional spherical shell, showing that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23930","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/2606.23930/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"}