{"paper":{"title":"A local contact systolic inequality in dimension three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Gabriele Benedetti, Jungsoo Kang","submitted_at":"2019-02-04T15:24:16Z","abstract_excerpt":"Let $\\alpha$ be a contact form on a connected closed three-manifold $\\Sigma$. The systolic ratio of $\\alpha$ is defined as $\\rho_{\\mathrm{sys}}(\\alpha):=\\tfrac{1}{\\mathrm{Vol}(\\alpha)}T_{\\min}(\\alpha)^2$, where $T_{\\min}(\\alpha)$ and $\\mathrm{Vol}(\\alpha)$ denote the minimal period of periodic Reeb orbits and the contact volume. The form $\\alpha$ is said to be Zoll if its Reeb flow generates a free $S^1$-action on $\\Sigma$. We prove that the set of Zoll contact forms on $\\Sigma$ locally maximises the systolic ratio in the $C^3$-topology. More precisely, we show that every Zoll form $\\alpha_*$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01249","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"}