scholarly journals Volume Growth and the Topology of Manifolds with Nonnegative Ricci Curvature

2010 ◽  
Vol 20 (3) ◽  
pp. 723-750 ◽  
Author(s):  
Michael Munn
Keyword(s):  
Ricci Curvature ◽  
Volume Growth ◽  
Nonnegative Ricci Curvature ◽  
Topology Of Manifolds

scholarly journals A Volume Comparison Estimate with Radially Symmetric Ricci Curvature Lower Bound and Its Applications

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Zisheng Hu ◽  
Yadong Jin ◽  
Senlin Xu
Keyword(s):  
Lower Bound ◽  
Ricci Curvature ◽  
Betti Number ◽  
Volume Growth ◽  
Topological Type ◽  
Volume Comparison ◽  
Nonnegative Ricci Curvature ◽  
Finite Topological Type

We extend the classical Bishop-Gromov volume comparison from constant Ricci curvature lower bound to radially symmetric Ricci curvature lower bound, and apply it to investigate the volume growth, total Betti number, and finite topological type of manifolds with nonasymptotically almost nonnegative Ricci curvature.

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

scholarly journals Lower bounds on Ricci flow invariant curvatures and geometric applications

2015 ◽  
Vol 2015 (703) ◽  
Author(s):  
Thomas Richard
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Lower Bounds ◽  
Ricci Flow ◽  
Nonnegative Curvature ◽  
Curvature Operator ◽  
Nonnegative Ricci Curvature ◽  
Invariant Cones

AbstractWe consider Ricci flow invariant cones 𝒞 in the space of curvature operators lying between the cones “nonnegative Ricci curvature” and “nonnegative curvature operator”. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to the Ricci flow has its curvature operator which satisfies

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