An isoperimetric inequality is a lower bound on the boundary measure of sets 
in terms of their measure. Finding the optimal sets (of given measure and of 
minimal boundary measure) is very difficult, and the only hope is to estimate 
the isoperimetric function. This is well understood on the line (Bobkov) and 
for the product of standard Gaussian measures (Sudakov-Tsirel'son, Borell). 
We shall recall these known results.

Then, we shall explain how functional inequalities can be used to get 
dimension free isoperimetric inequalities for measures between exponential 
and Gaussian. Also, using the transport of mass technique we shall dervive 
isoperimetric inequalities (depending on the dimension) for measures with 
tails larger than exponential.