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arXiv · 2302.02684

Poincar{\'e} inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures

Baptiste Nicolas Huguet
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Abstract

We obtain new sharp weighted Poincar{\'e} 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 Poincar{\'e} inequality for the whole range of parameters, with the optimal spectral gap, the error term and the extremal functions.

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Baptiste Nicolas Huguet. 2023-02-06. Poincar{\'e} inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures. https://arxiv.org/abs/2302.02684

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