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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2020 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2020
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211006 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862643934029676544 |
|---|---|
| author | Guo, Yifan |
| author_facet | Guo, Yifan |
| citation_txt | The Measure Preserving Isometry Groups of Metric Measure Spaces. Yifan Guo. SIGMA 16 (2020), 114, 14 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2026-03-15T09:12:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211006 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T09:12:28Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Guo, Yifan 2025-12-22T09:24:36Z 2020 The Measure Preserving Isometry Groups of Metric Measure Spaces. Yifan Guo. SIGMA 16 (2020), 114, 14 pages 1815-0659 2020 Mathematics Subject Classification: 53C20; 53C21; 53C23 arXiv:2006.04092 https://nasplib.isofts.kiev.ua/handle/123456789/211006 https://doi.org/10.3842/SIGMA.2020.114 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. The results in this article are mainly part of the author's undergraduate thesis at Tsinghua University. The author would like to express his sincere gratitude to Professor Jinxin Xue, who brought him into this field and gave him expert advice. He would also like to thank Professors Yann Brenier and Francois Bolley for their email of discussion and Professor Tapio Rajala for telling him the articles [17, 28] on the measure-preserving isometry groups of RCD spaces. Finally, he would like to thank the anonymous referees for their useful comments, which led to Theorem 1.7. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Measure Preserving Isometry Groups of Metric Measure Spaces Article published earlier |
| spellingShingle | The Measure Preserving Isometry Groups of Metric Measure Spaces Guo, Yifan |
| title | The Measure Preserving Isometry Groups of Metric Measure Spaces |
| title_full | The Measure Preserving Isometry Groups of Metric Measure Spaces |
| title_fullStr | The Measure Preserving Isometry Groups of Metric Measure Spaces |
| title_full_unstemmed | The Measure Preserving Isometry Groups of Metric Measure Spaces |
| title_short | The Measure Preserving Isometry Groups of Metric Measure Spaces |
| title_sort | measure preserving isometry groups of metric measure spaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211006 |
| work_keys_str_mv | AT guoyifan themeasurepreservingisometrygroupsofmetricmeasurespaces AT guoyifan measurepreservingisometrygroupsofmetricmeasurespaces |