JournalsjemsVol. 20, No. 5pp. 1055–1073

Characterising the big pieces of Lipschitz graphs property using projections

  • Henri Martikainen

    University of Helsinki, Finland
  • Tuomas Orponen

    University of Helsinki, Finland
Characterising the big pieces of Lipschitz graphs property using projections cover

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Abstract

We characterise the big pieces of Lipschitz graphs property in terms of projections. Roughly speaking, we prove that if a large subset of an nn-Ahlfors–David regular set ERdE \subset \mathbb R^d has plenty of projections in L2L^2, then a large part of EE is contained in a single Lipschitz graph. This is closely related to a question of G. David and S. Semmes.

Cite this article

Henri Martikainen, Tuomas Orponen, Characterising the big pieces of Lipschitz graphs property using projections. J. Eur. Math. Soc. 20 (2018), no. 5, pp. 1055–1073

DOI 10.4171/JEMS/782