# Diameter bounds for metric measure spaces with almost positive Ricci curvature and mean convex boundary

@article{Burtscher2020DiameterBF, title={Diameter bounds for metric measure spaces with almost positive Ricci curvature and mean convex boundary}, author={Annegret Y. Burtscher and Christian Ketterer and Robert J. McCann and Eric Woolgar}, journal={arXiv: Differential Geometry}, year={2020} }

Consider a metric measure space with non-negative Ricci curvature in the sense of Lott, Sturm and Villani. We prove a sharp upper bound on the diameter of any subset whose boundary has a positive lower bound on its generalized mean curvature. This provides a nonsmooth analog to a result of Kasue (1983) and Li (2014). We also prove a stability statement concerning such bounds.

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