Optimal subelliptic super-Poincar\'e and isoperimetric inequalities on stratified Lie groups
Abstract
We prove q-super-Poincar\'e inequalities, q ∈ [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.
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