Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds

@article{Cavalletti2015SharpGA,
  title={Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds},
  author={Fabio Cavalletti and Andrea Mondino},
  journal={arXiv: Metric Geometry},
  year={2015}
}
For metric measure spaces verifying the reduced curvature-dimension condition $CD^*(K,N)$ we prove a series of sharp functional inequalities under the additional assumption of essentially non-branching. Examples of spaces entering this framework are (weighted) Riemannian manifolds satisfying lower Ricci curvature bounds and their measured Gromov Hausdorff limits, Alexandrov spaces satisfying lower curvature bounds and more generally $RCD^*(K,N)$-spaces, Finsler manifolds endowed with a strongly… Expand
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TLDR
This work sharpen the inequalities obtained by Buser and Ledoux obtaining a dimension-free sharp Buser inequality for spaces with (Bakry-Émery weighted) Ricci curvature bounded below by K ∈ R (the inequality is sharp for K > 0 as equality is obtained on the Gaussian space). Expand
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