{"paper":{"title":"Bi-Lipschitz parts of quasisymmetric mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jonas Azzam","submitted_at":"2013-08-02T17:24:59Z","abstract_excerpt":"A natural quantity that measures how well a map $f:\\mathbb{R}^{d}\\rightarrow \\mathbb{R}^{D}$ is approximated by an affine transformation is \\[\\omega_{f}(x,r)=\\inf_{A}\\left(\\frac{1}{|B(x,r)|}\\int_{B(x,r)}\\left(\\frac{|f-A|}{|A'|r}\\right)^{2}\\right)^{\\frac{1}{2}},\\] where the infimum ranges over all non constant affine transformations. This is natural insofar as it is invariant under rescaling $f$ in either its domain or image. We show that if $f:\\mathbb{R}^{d}\\rightarrow \\mathbb{R}^{D}$ is quasisymmetric and its image has a sufficient amount of rectifiable structure (although not necessarily $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0558","kind":"arxiv","version":4},"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"}