Shaosai Huang, Xiaochun Rong, Bing Wang, “Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing”, SIGMA, 2020, том 16,123, 25 стр.

Эта публикация цитируется в 2 статьях

Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing

Shaosai Huang^a, Xiaochun Rong^b, Bing Wang^c

^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

Аннотация: 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.

Ключевые слова: almost flat manifold, collapsing geometry, locally bounded Ricci covering geometry, nilpotent Killing structure, Ricci flow.

MSC: 53C21, 53C23, 53E20

Поступила: 30 августа 2020 г.; в окончательном варианте 23 ноября 2020 г.; опубликована 30 ноября 2020 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2020.123