scholarly journals The almost rigidity of manifolds with lower bounds on Ricci curvature and minimal volume growth

2000 ◽  
Vol 8 (1) ◽  
pp. 159-212 ◽  
Author(s):  
Christina Sormani
Keyword(s):  
Ricci Curvature ◽  
Lower Bounds ◽  
Volume Growth ◽  
Minimal Volume ◽  
Almost Rigidity

Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products

1996 ◽  
Vol 144 (1) ◽  
pp. 189 ◽  
Author(s):  
Jeff Cheeger ◽  
Tobias H. Colding
Keyword(s):  
Ricci Curvature ◽  
Lower Bounds ◽  
Warped Products ◽  
Almost Rigidity

scholarly journals Greatest lower bounds on Ricci curvature of homogeneous toric bundles

2017 ◽  
Vol 28 (04) ◽  
pp. 1750024 ◽  
Author(s):  
Yi Yao
Keyword(s):  
Ricci Curvature ◽  
Lower Bounds ◽  
Line Bundles

We derive a formula of the greatest lower bounds on Ricci curvature of Fano homogeneous toric bundles. A criteria for the ampleness of line bundles over general homogeneous toric bundles is also obtained.

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

scholarly journals On the limit behavior of metrics in the continuity method for the Kähler–Einstein problem on a toric Fano manifold

2012 ◽  
Vol 148 (6) ◽  
pp. 1985-2003 ◽  
Author(s):  
Chi Li
Keyword(s):  
Ricci Curvature ◽  
Lower Bounds ◽  
Limit Behavior ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Continuity Method ◽  
Type Singularity ◽  
Moment Polytope ◽  
The Moment ◽  
Monge Ampere

AbstractThis work is a continuation of the author’s previous paper [Greatest lower bounds on the Ricci curvature of toric Fano manifolds, Adv. Math. 226 (2011), 4921–4932]. On any toric Fano manifold, we discuss the behavior of the limit metric of a sequence of metrics which are solutions to a continuity family of complex Monge–Ampère equations in the Kähler–Einstein problem. We show that the limit metric satisfies a singular complex Monge–Ampère equation. This gives a conic-type singularity for the limit metric. Information on conic-type singularities can be read off from the geometry of the moment polytope.

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