{"paper":{"title":"Hofer Geometry of a Subset of a Symplectic Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Fabian Ziltener, Jan Swoboda","submitted_at":"2011-02-24T01:20:17Z","abstract_excerpt":"To every closed subset $X$ of a symplectic manifold $(M,\\omega)$ we associate a natural group of Hamiltonian diffeomorphisms $Ham(X,\\omega)$. We equip this group with a semi-norm $\\Vert\\cdot\\Vert^{X,\\omega}$, generalizing the Hofer norm. We discuss $Ham(X,\\omega)$ and $\\Vert\\cdot\\Vert^{X,\\omega}$ if $X$ is a symplectic or isotropic submanifold. The main result involves the relative Hofer diameter of $X$ in $M$. Its first part states that for the unit sphere in $R^{2n}$ this diameter is bounded below by $\\frac\\pi2$, if $n\\geq2$. Its second part states that for $n\\geq2$ and $d\\geq n+1$ there exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4889","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"}