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

2024/11/20 by Yaozhong W. Qiu, Qiu, Yaozhong W. · 1 citation
Mathematics · #26D10 #60J60 #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2411.13430

openalex publication_date 2024/11/20 · openalex created_date 2024/11/24 · openalex updated_date 2026/07/28

Abstract

We prove q-super-Poincaré 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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• Almost isoperimetric extremisers of two subriemannian probability measures

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