{"paper":{"title":"On the $L^p$-geometry of autonomous Hamiltonian diffeomorphisms of surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Egor Shelukhin, Michael Brandenbursky","submitted_at":"2014-05-30T17:53:37Z","abstract_excerpt":"We prove a number of results on the interrelation between the $L^p$-metric on the group of Hamiltonian diffeomorphisms of surfaces and the subset of all autonomous Hamiltonian diffeomorphisms. More precisely, we show that there are Hamiltonian diffeomorphisms of all surfaces of genus $g\\neq 1$ lying arbitrarily $L^p$-far from this subset; answering a variant of a question of Polterovich for the $L^p$-metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7931","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"}