Uniform measures and uniform rectifiability

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)


© 2015 London Mathematical Society. In this paper, it is shown that if μ is an n-dimensional Ahlfors-David regular measure in ℝd which satisfies the so-called weak constant density condition, then μ 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 ℝd. In particular, it is shown here that they satisfy the 'big pieces of Lipschitz graphs' property.
Original languageEnglish
Pages (from-to)1-18
JournalJournal of the London Mathematical Society
Issue number1
Publication statusPublished - 1 Jan 2014


Dive into the research topics of 'Uniform measures and uniform rectifiability'. Together they form a unique fingerprint.

Cite this