Large volume growth and the topology of open manifolds

2002 ◽  
Vol 239 (3) ◽  
pp. 515-526 ◽  
Author(s):  
Changyu Xia
Keyword(s):  
Large Volume ◽  
Volume Growth ◽  
Open Manifolds ◽  
Large Volume Growth

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.

Volume growth of open manifolds with nonnegative curvature

1990 ◽  
Vol 8 (2) ◽  
pp. 159-165
Author(s):  
Viktor Schroeder ◽  
Martin Strake
Keyword(s):  
Volume Growth ◽  
Nonnegative Curvature ◽  
Open Manifolds
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