{"paper":{"title":"Constant mean curvature $k$-noids in homogeneous manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Julia Plehnert","submitted_at":"2013-06-02T15:29:22Z","abstract_excerpt":"For each $k\\geq2$, we construct two families of surfaces with constant mean curvature $H$ for $H\\in[0,1/2]$ in $\\Sigma(\\kappa)\\times\\R$ where $\\kappa+4H^2\\leq0$. The surfaces are invariant under $2\\pi/k$-rotations about a vertical fiber of $\\Sigma(\\kappa)\\times\\R$, have genus zero, and a finite number of ends. The first family generalizes the notion of $k$-noids: It has $k$ ends, one horizontal and $k$ vertical symmetry planes. The second family is less symmetric and has two types of ends. Each surface arises as the conjugate (sister) surface of a minimal graph in a homogeneous 3-manifold. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0219","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"}