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We consider a certain class of second order, variable coefficient divergenceform elliptic operators, in a uniform domain $\Omega$ with Ahlfors regularboundary, and we show that the $A_\infty$ property of the elliptic measureassociated to any such operator and its transpose imply that the domain is infact NTA (and hence chord-arc). The converse was already known, and followsfrom work of Kenig and Pipher.

$A_\infty$ implies NTA for a class of variable coefficient elliptic operators