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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
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.
Received: August 30, 2020; in final form November 23, 2020; Published online November 30, 2020
Citation:
Shaosai Huang, Xiaochun Rong, Bing Wang, “Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing”, SIGMA, 16 (2020), 123, 25 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1660 https://www.mathnet.ru/eng/sigma/v16/p123
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