  We present an asymptotic analysis of a mesoscale energy for bilayer membranes
that has been introduced and analyzed in two space dimensions by the second and
third author (Arch. Ration. Mech. Anal. 193, 2009). The energy is both
non-local and non-convex. It combines a surface area and a
Monge-Kantorovich-distance term, leading to a competition between preferences
for maximally concentrated and maximally dispersed configurations. Here we
extend key results of our previous analysis to the three dimensional case.
First we prove a general lower estimate and formally identify a curvature
energy in the zero-thickness limit. Secondly we construct a recovery sequence
and prove a matching upper-bound estimate.
