Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing
We survey some recent developments in the study of collapsing Riemannian manifolds with Ricci curvature bounded below, especially the locally bounded Ricci covering geometry and the Ricci flow smoothing techniques. We then prove that if a Calabi-Yau manifold is sufficiently volume collapsed with bou...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2020 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211096 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing. Shaosai Huang, Xiaochun Rong and Bing Wang. SIGMA 16 (2020), 123, 25 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862608144653352960 |
|---|---|
| author | Huang, Shaosai Rong, Xiaochun Wang, Bing |
| author_facet | Huang, Shaosai Rong, Xiaochun Wang, Bing |
| citation_txt | Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing. Shaosai Huang, Xiaochun Rong and Bing Wang. SIGMA 16 (2020), 123, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We survey some recent developments in the study of collapsing Riemannian manifolds with Ricci curvature bounded below, especially the locally bounded Ricci covering geometry and the Ricci flow smoothing techniques. We then prove that if a Calabi-Yau manifold is sufficiently volume collapsed with bounded diameter and sectional curvature, then it admits a Ricci-flat Kähler metric together with a compatible pure nilpotent Killing structure: this is related to an open question of Cheeger, Fukaya, and Gromov.
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| first_indexed | 2026-03-14T05:22:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211096 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T05:22:31Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Huang, Shaosai Rong, Xiaochun Wang, Bing 2025-12-23T13:14:10Z 2020 Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing. Shaosai Huang, Xiaochun Rong and Bing Wang. SIGMA 16 (2020), 123, 25 pages 1815-0659 2020 Mathematics Subject Classification: 53C21; 53C23; 53E20 arXiv:2008.12419 https://nasplib.isofts.kiev.ua/handle/123456789/211096 https://doi.org/10.3842/SIGMA.2020.123 We survey some recent developments in the study of collapsing Riemannian manifolds with Ricci curvature bounded below, especially the locally bounded Ricci covering geometry and the Ricci flow smoothing techniques. We then prove that if a Calabi-Yau manifold is sufficiently volume collapsed with bounded diameter and sectional curvature, then it admits a Ricci-flat Kähler metric together with a compatible pure nilpotent Killing structure: this is related to an open question of Cheeger, Fukaya, and Gromov. The second author was partially supported by NSFC Grant 11821101, Beijing Natural Science Foundation Z19003, and a research fund from Capital Normal University. The third author is partially supported by the General Program of the National Natural Science Foundation of China (Grant No. 11971452) and a research fund of USTC. The authors would like to thank anonymous referees for their careful proofreading and helpful comments on the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing Article published earlier |
| spellingShingle | Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing Huang, Shaosai Rong, Xiaochun Wang, Bing |
| title | Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing |
| title_full | Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing |
| title_fullStr | Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing |
| title_full_unstemmed | Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing |
| title_short | Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing |
| title_sort | collapsing geometry with ricci curvature bounded below and ricci flow smoothing |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211096 |
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