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.

scholarly journals Ricci curvature and volume growth

1991 ◽  
Vol 148 (1) ◽  
pp. 161-167
Author(s):  
Martin Strake ◽  
Gerard Walschap
Keyword(s):  
Ricci Curvature ◽  
Volume Growth

Gradient Estimates for Harmonic Functions on Manifolds With Lipschitz Metrics

1998 ◽  
Vol 50 (6) ◽  
pp. 1163-1175 ◽  
Author(s):  
Jingyi Chen ◽  
Elton P. Hsu
Keyword(s):  
Ricci Curvature ◽  
Harmonic Functions ◽  
Volume Growth ◽  
Gradient Estimate ◽  
Gradient Estimates ◽  
Smooth Manifolds ◽  
Lipschitz Continuous ◽  
Bounded Below

AbstractWe introduce a distributional Ricci curvature on complete smooth manifolds with Lipschitz continuous metrics. Under an assumption on the volume growth of geodesics balls, we obtain a gradient estimate for weakly harmonic functions if the distributional Ricci curvature is bounded below.

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