{"paper":{"title":"Strongly stable surfaces in sub-Riemannian $3$-space forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Ana Hurtado, C\\'esar Rosales","submitted_at":"2016-10-14T11:15:11Z","abstract_excerpt":"A surface of constant mean curvature (CMC) equal to $H$ in a sub-Riemannian $3$-manifold is strongly stable if it minimizes the functional $\\text{area}+2H\\,\\text{volume}$ up to second order. In this paper we obtain some criteria ensuring strong stability of surfaces in Sasakian $3$-manifolds. We also produce new examples of $C^1$ complete CMC surfaces with empty singular set in the sub-Riemannian $3$-space forms by studying those ones containing a vertical line. As a consequence, we are able to find complete strongly stable non-vertical surfaces with empty singular set in the sub-Riemannian hy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04408","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":""},"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"}