Isoperimetric inequality in noncompact MCP spaces

@inproceedings{Cavalletti2021IsoperimetricII,
  title={Isoperimetric inequality in noncompact MCP spaces},
  author={Fabio Cavalletti and Davide Manini},
  year={2021}
}
We prove a sharp isoperimetric inequality for the class of metric measure spaces verifying the synthetic Ricci curvature lower bounds MCP(0, N) and having Euclidean volume growth at infinity. We avoid the classical use of the Brunn-Minkowski inequality, not available for MCP(0, N), and of the PDE approach, not available in the singular setting. Our approach will be carried over by using a scaling limit of localization. 
A sharp isoperimetric inequality in metric measure spaces with non-negative Ricci curvature
  • Bang-Xian Han
  • Mathematics
  • 2021
We prove a sharp dimension-free isoperimetric inequality, involving the volume entropy, in non-compact metric measure spaces with non-negative synthetic Ricci curvature.

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