{"paper":{"title":"Sharp geometric rigidity of isometries on Heisenberg groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"D. V. Isangulova, S. K. Vodopyanov","submitted_at":"2012-04-16T11:15:25Z","abstract_excerpt":"We prove sharp geometric rigidity estimates for isometries on Heisenberg groups. Our main result asserts that every $(1+\\varepsilon)$-quasi-isometry on a John domain of the Heisenberg group $\\mathbb{H}^n$, $n>1$, is close to some isometry up to proximity order $\\sqrt{\\varepsilon}+\\varepsilon$ in the uniform norm, and up to proximity order $\\varepsilon$ in the $L_p^1$-norm. We give examples showing the asymptotic sharpness of our results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3441","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"}