Optimal subelliptic super-Poincaré and isoperimetric inequalities on stratified Lie groups

We prove $q$-super-Poincaré inequalities, $q\in [1,2]$, for a class of exponential power type probability measures defined in terms of a norm in a number of subelliptic settings, primarily on stratified Lie groups but also in the Grushin and Heisenberg-Greiner settings. Our results include generically optimal isoperimetric inequalities for such probability measures.