  In this paper we establish optimal isoperimetric inequalities for a nonlocal
perimeter adapted to the fractional powers of a class of
Kolmogorov-Fokker-Planck operators which are of interest in physics. These
operators are very degenerate and do not possess a variational structure. The
prototypical example was introduced by Kolmogorov in his 1938 paper on brownian
motion and the theory of gases. Our work has been influenced by ideas of M.
Ledoux in the local case.
