Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908578663628800 |
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| author | Caputo, Emanuele Nobili, Francesco Rossi, Tommaso |
| author_facet | Caputo, Emanuele Nobili, Francesco Rossi, Tommaso |
| contents | We study comparison estimates on metric measure spaces admitting a synthetic variable Ricci curvature lower bound. We obtain geometric and functional inequalities assuming that the deficit of the lower bound from a given constant is sufficiently integrable. More precisely, we extend to the nonsmooth setting the Bishop-Gromov comparison, the Myers' diameter estimate and the Cheng's comparison principle for Dirichlet eigenvalues. Our analysis relies on the localization method and on one-dimensional comparison estimates for nonsmooth weighted intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization Caputo, Emanuele Nobili, Francesco Rossi, Tommaso Metric Geometry Differential Geometry 53C23, 49Q22, 58E99 We study comparison estimates on metric measure spaces admitting a synthetic variable Ricci curvature lower bound. We obtain geometric and functional inequalities assuming that the deficit of the lower bound from a given constant is sufficiently integrable. More precisely, we extend to the nonsmooth setting the Bishop-Gromov comparison, the Myers' diameter estimate and the Cheng's comparison principle for Dirichlet eigenvalues. Our analysis relies on the localization method and on one-dimensional comparison estimates for nonsmooth weighted intervals. |
| title | Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization |
| topic | Metric Geometry Differential Geometry 53C23, 49Q22, 58E99 |
| url | https://arxiv.org/abs/2509.22514 |