We study the inflated phase of two dimensional lattice polygons, both convex and column-convex, with fixed area A and variable perimeter, when a weight μ exp[−Jb] is associated to a polygon with perimeter t and b bends. The mean perimeter is calculated as a function of the fugacity μ and the bending rigidity J . In the limit μ → 0, the mean perimeter has the asymptotic behaviour 〈t〉/4 √ A ≃ 1−K...
