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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
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| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | 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 |
| Цитувати: | The Measure Preserving Isometry Groups of Metric Measure Spaces. Yifan Guo. SIGMA 16 (2020), 114, 14 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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.
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| ISSN: | 1815-0659 |