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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 123, 25 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.123 (Mi sigma1660) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing

Shaosai Huanga, Xiaochun Rongb, Bing Wangc

a Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA
b Department of Mathematics, Rutgers University, New Brunswick, NJ 08854, USA
c Institute of Geometry and Physics, and School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui Province, 230026, China
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DOI: https://doi.org/10.3842/SIGMA.2020.123
Abstract: 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.
Keywords: almost flat manifold, collapsing geometry, locally bounded Ricci covering geometry, nilpotent Killing structure, Ricci flow.
Funding agency Grant number
National Natural Science Foundation of China 11821101
Beijing Natural Science Foundation Z19003
National Natural Science Foundation of China 11971452
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.
Received: August 30, 2020; in final form November 23, 2020; Published online November 30, 2020
Bibliographic databases:
Document Type: Article
MSC: 53C21, 53C23, 53E20
Language: English
Citation: Shaosai Huang, Xiaochun Rong, Bing Wang, “Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing”, SIGMA, 16 (2020), 123, 25 pp.
Citation in format AMSBIB
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\paper Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing
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