{"paper":{"title":"Minimal immersions of closed surfaces in hyperbolic three-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.GT"],"primary_cat":"math.DG","authors_text":"Marcello Lucia, Zheng Huang","submitted_at":"2010-11-05T02:41:01Z","abstract_excerpt":"We study minimal immersions of closed surfaces (of genus $g \\ge 2$) in hyperbolic 3-manifolds, with prescribed data $(\\sigma, t\\alpha)$, where $\\sigma$ is a conformal structure on a topological surface $S$, and $\\alpha dz^2$ is a holomorphic quadratic differential on the surface $(S,\\sigma)$. We show that, for each $t \\in (0,\\tau_0)$ for some $\\tau_0 > 0$, depending only on $(\\sigma, \\alpha)$, there are at least two minimal immersions of closed surface of prescribed second fundamental form $Re(t\\alpha)$ in the conformal structure $\\sigma$. Moreover, for $t$ sufficiently large, there exists no "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1313","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"}