The Measure Preserving Isometry Groups of Metric Measure Spaces

Bochner's theorem says that if is a compact Riemannian manifold with negative Ricci curvature, then the isometry group Iso() is finite. In this article, we show that if (, , ) is a compact metric measure space with synthetic negative Ricci curvature in Sturm's sense, then the measure-pres...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2020
1. Verfasser: Guo, Yifan
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2020
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/211006
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:The Measure Preserving Isometry Groups of Metric Measure Spaces. Yifan Guo. SIGMA 16 (2020), 114, 14 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung:Bochner's theorem says that if is a compact Riemannian manifold with negative Ricci curvature, then the isometry group Iso() is finite. In this article, we show that if (, , ) is a compact metric measure space with synthetic negative Ricci curvature in Sturm's sense, then the measure-preserving isometry group Iso(, , ) 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.
ISSN:1815-0659