Poincaré inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures
Résumé
We obtain new sharp weighted Poincaré inequalities for convex measures on Riemannian manifolds. When specified to generalised Cauchy measures, it 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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