Abstract
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.
Funding Statement
This research is partially supported by the Centre Henri Lebesgue (ANR-11-LABX-0020-0) and the ANR project RAGE “Analyse Réelle et Géométrie” (ANR-18-CE40-0012).
Acknowledgments
We would like to thank François Bolley for his encouragements and for our many useful discussions. We also thank Geneviève Ropars for her helpful suggestions.
Citation
Baptiste Huguet. "Poincaré inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures." Bernoulli 30 (3) 2207 - 2227, August 2024. https://doi.org/10.3150/23-BEJ1670
