$A_\infty$ implies NTA for a class of variable coefficient elliptic   operators
  We consider a certain class of second order, variable coefficient divergence form elliptic operators, in a uniform domain $\Omega$ with Ahlfors regular boundary, and we show that the $A_\infty$ property of the elliptic measure associated to any such operator and its transpose imply that the domain is in fact NTA (and hence chord-arc). The converse was already known, and follows from work of Kenig and Pipher. 
Steve Hofmann, Jos\'e Mar\'ia Martell, Tatiana Toro
math.CA math.AP