Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing
Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing
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Ricci曲率下有界的折叠几何与Ricci流光滑
DOI：
10.3842/sigma.2020.123
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发表时间：
2020-08
期刊：
影响因子：
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通讯作者：
S. Huang;Xiaochun Rong;B. Wang
中科院分区：
文献类型：
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作者：
S. Huang;Xiaochun Rong;B. Wang
本文综述了具有Ricci曲率有界的坍缩黎曼流形的最新研究进展，特别是局部有界的Ricci覆盖几何和Ricci流平滑技术。然后，我们证明了如果一个Calabi-Yau流形在有界直径和截面曲率下是充分体积坍缩的，那么它就允许一个Ricci-flat Kähler度量和一个相容的纯幂零的Killing结构：这与Cheeger、Fukaya和Gromov的一个开放问题有关。
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 metrictogether with a compatible pure nilpotent Killing structure: this is related to an open question of Cheeger, Fukaya and Gromov.