On the uniform rectifiability of AD regular measures with bounded Riesz   transform operator: the case of codimension 1
  We prove that if $\mu$ is a d-dimensional Ahlfors-David regular measure in $\R^{d+1}$, then the boundedness of the $d$-dimensional Riesz transform in $L^2(\mu)$ implies that the non-BAUP David-Semmes cells form a Carleson family. Combined with earlier results of David and Semmes, this yields the uniform rectifiability of $\mu$. 
Fedor Nazarov, Xavier Tolsa, Alexander Volberg
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