论文标题
折叠几何形状以下面的RICCI曲率和RICCI流平滑为
Collapsing geometry with Ricci curvature bounded below and Ricci flow smoothing
论文作者
论文摘要
我们调查了下面有RICCI曲率崩溃的Riemannian歧管研究中的一些最新发展，尤其是覆盖几何形状和RICCI流平滑技术的本地界限Ricci。然后，我们证明，如果卡拉比远的歧管与有界直径和截面曲率充分崩溃，那么它将接受一个带有兼容的纯净尼尔犬的杀戮结构的ricci-flatKählerMetrictect，这与脸颊，福卡亚和格罗莫夫的开放问题有关。
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.
