scholarly journals Complete manifolds with nonnegative Ricci curvature and almost best Sobolev constant

2001 ◽  
Vol 45 (4) ◽  
pp. 1253-1259 ◽  
Author(s):  
Changyu Xia
Keyword(s):  
Ricci Curvature ◽  
Nonnegative Ricci Curvature ◽  
Sobolev Constant ◽  
Complete Manifolds

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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