  In the present paper, we show that for an optimal class of elliptic operators
with non-smooth coefficients on a 1-sided Chord-Arc domain, the boundary of the
domain is uniformly rectifiable if and only if the Green function $G$ behaves
like a distance function to the boundary, in the sense that $\Big|\frac{\nabla
G(X)}{G(X)}-\frac{\nabla D(X)}{D(X)}\Big|^2D(X) dX$ is the density of a
Carleson measure, where $D$ is a regularized distance adapted to the boundary
of the domain. The main ingredient in our proof is a corona decomposition that
is compatible with Tolsa's $\alpha$-number of uniformly rectifiable sets. We
believe that the method can be applied to many other problems at the
intersection of PDE and geometric measure theory, and in particular, we are
able to derive a generalization of the classical F. and M. Riesz theorem to the
same class of elliptic operators as above.
