Plenty of big projections imply big pieces of Lipschitz graphs

Abstract

I prove that a closed $n$-regular set $E\subset {\mathbb{R}}^d$ with plenty of big projections has big pieces of Lipschitz graphs. This answers a question of David and Semmes.

arXiv comment40 pages. v3: referee comments incorporated

References in corpus (5)

• Rectifiability of harmonic measure
• A quantitative version of the Besicovitch projection theorem via multiscale analysis
• Uniform rectifiability from Carleson measure estimates and $\epsilon$-approximability of bounded harmonic functions
• Characterising the big pieces of Lipschitz graphs property using projections
• Semi-uniform domains and the $A_{\infty }$ property for harmonic measure

Cited by in corpus (6)

• Structure of sets with nearly maximal Favard length
• Cones, rectifiability, and singular integral operators
• Two examples related to conical energies
• Analytic capacity and dimension of sets with plenty of big projections
• Interactions between quantitative rectifiability, singular integrals, and boundary value problems for harmonic functions
• A note on the Hausdorff dimension of uniformly non flat sets with plenty of big projections