Corpus ID: 218665702

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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