Isoperimetric inequalities for subriemannian analogues of the gaussian measure

par Yaozhong Qiu (Paris Nanterre)

lundi 16 févr. 2026, 14:00 → 15:00 Europe/Paris

Amphi Schwartz

We propose a family of probability measures defined on a stratified Lie group, as well as on the Grushin and Heisenberg-Greiner spaces, which may be considered an analogue of the gaussian measure. As evidence, we show such measures satisfy an approximate (up to a constant) isoperimetric inequality, which is degenerate in the sense there is a mismatch between the decay of tails and isoperimetric profiles, and we show in two cases the corresponding approximate isoperimetric extremisers can be interpreted as a generalisation of a half-space. Along the way we will discuss some literature surrounding functional inequalities for probability measures in subriemannian settings, aspects of the proof, and finally a discussion on subsequent questions.