This paper contains a proof of the fact that doubling, linearly connected metric spaces are quasi-arc connected. It is a new and short proof of a theorem of Tukia.
We show that if a complete, doubling metric space is annulus linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, hyperbolic groups whose boundaries have no local cut points have conformal dimension greater than one; this answers a question of Bonk and Kleiner.