{"paper":{"title":"A local systolic-diastolic inequality in contact and symplectic geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.DS"],"primary_cat":"math.SG","authors_text":"Gabriele Benedetti, Jungsoo Kang","submitted_at":"2018-01-02T03:07:40Z","abstract_excerpt":"Let $\\Sigma$ be a connected closed three-manifold, and let $t_\\Sigma$ be the order of the torsion subgroup of $H_1(\\Sigma;\\mathbb Z)$. For a contact form $\\alpha$ on $\\Sigma$, we denote by $\\mathrm{Volume}(\\alpha)$ the contact volume of $\\alpha$, and by $T_{\\min}(\\alpha)$ and $T_{\\max}(\\alpha)$ the minimal period and the maximal period of prime periodic orbits of the Reeb flow of $\\alpha$ respectively. We say that $\\alpha$ is Zoll if its Reeb flow generates a free $S^1$-action on $\\Sigma$. We prove that every Zoll contact form $\\alpha_*$ on $\\Sigma$ admits a $C^3$-neighbourhood $\\mathcal U$ in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00539","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"}