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Pré-Publication, Document De Travail Année : 2023

Poincaré inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures

Résumé

We obtain new sharp weighted Poincaré inequalities on Riemannian manifolds for a general class of measures. When specialised to generalised Cauchy measures, this gives a unified and simple proof of the weighted Poincaré inequality for the whole range of parameters, with the optimal spectral gap, the error term and the extremal functions.
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Dates et versions

hal-03973129 , version 1 (03-02-2023)
hal-03973129 , version 2 (12-01-2024)

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Baptiste Nicolas Huguet. Poincaré inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures. 2023. ⟨hal-03973129v2⟩
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