Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization
Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Caputo, Emanuele, Nobili, Francesco, Rossi, Tommaso
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416830864
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