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arXiv · 2509.22514

Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization

Emanuele Caputo·Francesco Nobili·Tommaso Rossi
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Abstract

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.

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Emanuele Caputo, Francesco Nobili, Tommaso Rossi. 2025-09-26. Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization. https://arxiv.org/abs/2509.22514

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