{"paper":{"title":"A new pinching theorem for complete self-shrinkers and its generalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hongwei Xu, Li Lei, Zhiyuan Xu","submitted_at":"2017-12-05T20:12:43Z","abstract_excerpt":"In this paper, we firstly verify that if $M$ is a complete self-shrinker with polynomial volume growth in $\\mathbb{R}^{n+1}$, and if the squared norm of the second fundamental form of $M$ satisfies $0\\leq|A|^2-1\\leq\\frac{1}{18}$, then $|A|^2\\equiv1$ and $M$ is a round sphere or a cylinder. More generally, let $M$ be a complete $\\lambda$-hypersurface with polynomial volume growth in $\\mathbb{R}^{n+1}$ with $\\lambda\\neq0$. Then we prove that there exists an positive constant $\\gamma$, such that if $|\\lambda|\\leq\\gamma$ and the squared norm of the second fundamental form of $M$ satisfies $0\\leq|A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01899","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"}