Poincar{é} inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929209207685120 |
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| author | Huguet, Baptiste Nicolas |
| author_facet | Huguet, Baptiste Nicolas |
| contents | 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 and simple proof of the weighted Poincar{é} inequality for the whole range of parameters, with the optimal spectral gap, the error term and the extremal functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02684 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Poincar{é} inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures Huguet, Baptiste Nicolas Functional Analysis Probability 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 and simple proof of the weighted Poincar{é} inequality for the whole range of parameters, with the optimal spectral gap, the error term and the extremal functions. |
| title | Poincar{é} inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures |
| topic | Functional Analysis Probability |
| url | https://arxiv.org/abs/2302.02684 |