Complete manifolds with nonnegative Ricci curvature and large volume growth

1996 ◽  
Vol 125 (3) ◽  
pp. 393-404 ◽  
Author(s):  
Zhongmin Shen
Keyword(s):  
Ricci Curvature ◽  
Large Volume ◽  
Volume Growth ◽  
Nonnegative Ricci Curvature ◽  
Large Volume Growth ◽  
Complete Manifolds

Ricci curvature, radial curvature and large volume growth

2010 ◽  
Vol 150 (1) ◽  
pp. 63-74 ◽  
Author(s):  
Guanghan Li ◽  
Yi Shi ◽  
Chuanxi Wu
Keyword(s):  
Ricci Curvature ◽  
Large Volume ◽  
Volume Growth ◽  
Radial Curvature ◽  
Large Volume Growth

COMPLETE MANIFOLDS WITH SECTIONAL CURVATURE BOUNDED BELOW AND LARGE VOLUME GROWTH

2002 ◽  
Vol 34 (2) ◽  
pp. 229-235 ◽  
Author(s):  
CHANGYU XIA
Keyword(s):  
Riemannian Manifold ◽  
Sectional Curvature ◽  
Hyperbolic Space ◽  
Large Volume ◽  
Volume Growth ◽  
Large Volume Growth ◽  
Complete Manifolds ◽  
Bounded Below

This paper provides a proof that an n-dimensional complete open Riemannian manifold M with sectional curvature KM [ges ] −1 is diffeomorphic to a Euclidean n-space Rn if the volume growth of geodesic balls in M is close to that of the balls in an n-dimensional hyperbolic space Hn(−1) of sectional curvature −1.

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