Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature
@article{Balogh2022SharpIA, title={Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature}, author={Zolt'an M. Balogh and Alexandru Krist'aly}, journal={Mathematische Annalen}, year={2022} }
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 ndimensional 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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≥
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Ric
≥
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1
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