{"paper":{"title":"Stability of Catenoids and Helicoids in Hyperbolic Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Biao Wang","submitted_at":"2016-08-06T21:26:15Z","abstract_excerpt":"In this paper, we study the stability of catenoids and helicoids in the hyperbolic $3$-space $\\mathbb{H}^3$.\n  (1) For a family of spherical minimal catenoids $\\{\\mathcal{C}_a\\}_{a>0}$ in $\\mathbb{H}^3$, there exist two constants $0<a_c<a_l$ such that\n  $\\bullet$ $\\mathcal{C}_a$ is an unstable minimal surface with index one if $a<a_c$,\n  $\\bullet$ $\\mathcal{C}_a$ is a globally stable minimal surface if $a\\geq{}a_c$, and\n  $\\bullet$ $\\mathcal{C}_a$ is a least area minimal surface in the sense of Meeks and Yau if $a\\geq{}a_l$.\n  (2) For a family of minimal helicoids $\\{\\mathcal{H}_{\\bar{a}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02156","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"}