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The Measure Preserving Isometry Groups of Metric Measure Spaces
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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Bochner's theorem says that if $M$ is a compact Riemannian manifold with negative Ricci curvature, then the isometry group $\operatorname{Iso}(M)$ is finite. In this article, we show that if $(X,d,m)$ is a compact metric measure space with synthetic negative Ricci curvature in Sturm's sense, then the measure preserving isometry group $\operatorname{Iso}(X,d,m)$ is finite. We also give an effective estimate on the order of the measure preserving isometry group for a compact weighted Riemannian manifold with negative Bakry–Émery Ricci curvature except for small portions.
Keywords: synthetic Ricci curvature, metric measure space, Bochner's theorem, measure preserving isometry.
Mots-clés : optimal transport 
@article{SIGMA_2020_16_a113,
     author = {Yifan Guo},
     title = {The {Measure} {Preserving} {Isometry} {Groups} of {Metric} {Measure} {Spaces}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2020},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a113/}
}
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Yifan Guo. The Measure Preserving Isometry Groups of Metric Measure Spaces. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a113/

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