{"paper":{"title":"Slicing a 2-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Yevgeny Liokumovich","submitted_at":"2013-12-31T00:39:36Z","abstract_excerpt":"We show that for every complete Riemannian surface $M$ diffeomorphic to a sphere with $k \\geq 0$ holes there exists a Morse function $f:M \\rightarrow \\mathbb{R}$, which is constant on each connected component of the boundary of $M$ and has fibers of length no more than $52 \\sqrt{Area(M)}+length(\\partial M)$. We also show that on every 2-sphere there exists a simple closed curve of length $\\leq 26 \\sqrt{Area(S^2)}$ subdividing the sphere into two discs of area $\\geq \\frac{1}{3}Area(S^2)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0060","kind":"arxiv","version":2},"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"}