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math.FA2024
Logarithmic Sobolev inequalities for generalised Cauchy measures
Baptiste Nicolas Huguet
We prove a curvature-dimension criterion and obtain logarithmic Sobolev inequalities for generalised Cauchy measures with optimal weights and explicit constants. In the one-dimensi…
math.FA2023
Poincar{é} inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures
Baptiste Nicolas Huguet
We obtain new sharp weighted Poincar{é} inequalities on Riemannian manifolds for a general class of measures. When specialised to generalised Cauchy measures, this gives a unified…
math.FA2019
Intertwining relations for diffusions in manifolds and applications to functional inequalities
Baptiste Huguet
We prove intertwining relations by twisted gradients for Markov semi-groups. These relations are applied to Brascamp-Lieb type inequalities and spectral gap results. It generalizes…