Stability of isoperimetric type inequalities for some Monge–Ampère functionals

We investigate the stability of some inequalities of isoperimetric type related to
Monge–Ampère functionals. In particular, firstly we prove the stability of a reverse Faber–
Krahn inequality for the Monge–Ampère eigenvalue and its generalization. Then we give
a stability result for the Brunn–Minkowski inequality and for a consequent Urysohn’s type
inequality for the so-called n-torsional rigidity, a natural extension of the usual torsional
rigidity.