{"paper":{"title":"Self-Shrinkers With Second Fundamental Form of Constant Length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Qiang Guang","submitted_at":"2014-05-16T16:21:41Z","abstract_excerpt":"In this note, we give a new and simple proof of a result in {\\cite{DX1}} which states that any smooth complete self-shrinker in $\\mathbb{R}^3$ with second fundamental form of constant length must be a generalized cylinder $\\mathbb{S}^k \\times \\mathbb{R}^{2-k}$ for some $k\\leq2$. Moreover, we prove a gap theorem for smooth self-shrinkers in all dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4230","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"}