  In a recent paper A. Cianchi, N. Fusco, F. Maggi, and A. Pratelli have shown
that, in the Gauss space, a set of given measure and almost minimal Gauss
boundary measure is necessarily close to be a half-space. Using only geometric
tools, we extend their result to all symmetric log-concave measures \mu on the
real line. We give sharp quantitative isoperimetric inequalities and prove that
among sets of given measure and given asymmetry (distance to half line, i.e.
distance to sets of minimal perimeter), the intervals or complements of
intervals have minimal perimeter.
