Collapsed manifolds with Ricci bounded covering geometry

Collapsed manifolds with Ricci bounded covering geometry

We study collapsed manifolds with Ricci bounded covering geometry, i.e., Ricci curvature is bounded below and the Riemannian universal cover is non-collapsed or consists of uniform Reifenberg points. Applying the techniques in the Ricci flow, we partially extend the nilpotent structural results of C...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Transactions of the American Mathematical Society 2020-11, Vol.373 (11), p.8039-8057
Hauptverfasser: Huang, Hongzhi, Kong, Lingling, Rong, Xiaochun, Xu, Shicheng
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Physical Sciences
Science & Technology
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We study collapsed manifolds with Ricci bounded covering geometry, i.e., Ricci curvature is bounded below and the Riemannian universal cover is non-collapsed or consists of uniform Reifenberg points. Applying the techniques in the Ricci flow, we partially extend the nilpotent structural results of Cheeger-Fukaya-Gromov, on the collapsed manifolds with (sectional curvature) local bounded covering geometry, to the manifolds with (global) Ricci bounded covering geometry.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8177