Optimal subelliptic super-Poincar\'e and isoperimetric inequalities on stratified Lie groups

TL;DR

This paper establishes optimal super-Poincaré and isoperimetric inequalities for certain probability measures in subelliptic settings, including stratified Lie groups, Grushin, and Heisenberg-Greiner spaces.

Contribution

It introduces new super-Poincaré inequalities for exponential power measures on stratified Lie groups and related subelliptic spaces, with optimal isoperimetric inequalities.

Findings

Proved q-super-Poincaré inequalities for measures on stratified Lie groups.

Derived generically optimal isoperimetric inequalities for these measures.

Extended results to Grushin and Heisenberg-Greiner settings.

Abstract

We prove $q$-super-Poincar\'e 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.