{"paper":{"title":"A variational characterization of calibrated submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Da Rong Cheng, Jesse Madnick, Spiro Karigiannis","submitted_at":"2022-04-19T00:05:44Z","abstract_excerpt":"Let $M$ be a fixed compact oriented embedded submanifold of a manifold $\\overline{M}$. Consider the volume $\\mathcal{V} (\\overline{g}) = \\int_M \\mathsf{vol}_{(M, g)}$ as a functional of the ambient metric $\\overline{g}$ on $\\overline{M}$, where $g = \\overline{g}|_M$. We show that $\\overline{g}$ is a critical point of $\\mathcal{V}$ with respect to a special class of variations of $\\overline{g}$, obtained by varying a calibration $\\mu$ on $\\overline{M}$ in a particular way, if and only if $M$ is calibrated by $\\mu$. We do not assume that the calibration is closed. We prove this for almost comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.08591","kind":"arxiv","version":2},"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/2204.08591/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"}