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 |
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| 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| Summary: | 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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| ISSN: | 1815-0659 |