{"paper":{"title":"Closed Mean Curvature Self-Shrinking Surfaces of Generalized Rotational Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Peter McGrath","submitted_at":"2015-07-02T18:13:34Z","abstract_excerpt":"For each $n\\geq 2$ we construct a new closed embedded mean curvature self-shrinking hypersurface in $\\mathbb{R}^{2n}$. These self-shrinkers are diffeomorphic to $S^{n-1}\\times S^{n-1}\\times S^1$ and are $SO(n)\\times SO(n)$ invariant. The method is inspired by constructions of Hsiang and these surfaces generalize self-shrinking \"tori\" diffeomorphic to $S^{n-1}\\times S^1$ constructed by Angenent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00681","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"}