{"paper":{"title":"Uniform measures and uniform rectifiability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Xavier Tolsa","submitted_at":"2013-10-02T11:00:11Z","abstract_excerpt":"In this paper it is shown that if $\\mu$ is an n-dimensional Ahlfors-David regular measure in $R^d$ which satisfies the so-called weak constant density condition, then $\\mu$ is uniformly rectifiable. This had already been proved by David and Semmes in the cases n=1, 2 and d-1, and it was an open problem for other values of n. The proof of this result relies on the study of the n-uniform measures in $R^d$. In particular, it is shown here that they satisfy the \"big pieces of Lipschitz graphs\" property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0658","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"}