  We provide a potential theoretic characterization of vanishing chord-arc
domains under minimal assumptions. In particular we show that, if a domain has
Ahlfors regular boundary, the oscillation of the logarithm of the interior and
exterior Poisson kernels yields a great deal of geometric information about the
domain. We use techniques from the classical calculus of variations, potential
theory, quantitative geometric measure theory to accomplish this. One feature
of this work, compared to Bortz-Hofmann PAMS 16 and Kenig-Toro Crelle 06, is
that a priori we only require that the domains in question are connected.
