Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature

  title={Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature},
  author={Zolt'an M. Balogh and Alexandru Krist'aly},
  journal={Mathematische Annalen},
By using optimal mass transport theory we prove a sharp isoperimetric inequality in CD(0, N) metric measure spaces assuming an asymptotic volume growth at infinity. Our result extends recently proven isoperimetric inequalities for normed spaces and Riemannian manifolds to a nonsmooth framework. In the case of n-dimensional Riemannian manifolds with nonnegative Ricci curvature, we outline an alternative proof of the rigidity result of S. Brendle (2021). As applications of the isoperimetric… 
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