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.

scholarly journals A Note on Finsler Version of Calabi-Yau Theorem

2018 ◽  
Vol 2018 ◽  
pp. 1-4
Author(s):  
Songting Yin ◽  
Ruixin Wang ◽  
Pan Zhang
Keyword(s):  
Ricci Curvature ◽  
Volume Growth ◽  
Finsler Manifold ◽  
Infinite Volume ◽  
Growth Theorem ◽  
Negative Function ◽  
Weighted Ricci Curvature ◽  
Bounded Below

We generalize Calabi-Yau’s linear volume growth theorem to Finsler manifold with the weighted Ricci curvature bounded below by a negative function and show that such a manifold must have infinite volume.

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
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