{"paper":{"title":"Stability of submanifolds with parallel mean curvature in calibrated manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Isabel M.C. Salavessa","submitted_at":"2009-11-24T18:12:07Z","abstract_excerpt":"On a Riemannian manifold $\\bar{M}^{m+n}$ with an $(m+1)$-calibration $\\Omega$, we prove that an $m$-submanifold $M$ with constant mean curvature $H$ and calibrated extended tangent space $\\mathbb{R}H\\oplus TM$ is a critical point of the area functional for variations that preserve the enclosed $\\Omega$-volume. This recovers the case described by Barbosa, do Carmo and Eschenburg, when $n=1$ and $\\Omega$ is the volume element of $\\bar{M}$. To the second variation we associate an $\\Omega$-Jacobi operator and define $\\Omega$-stablility. Under natural conditions, we prove that the Euclidean $m$-sph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4689","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}