scholarly journals A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature bound

2014 ◽  
Vol 266 (6) ◽  
pp. 3741-3771 ◽  
Author(s):  
YanYan Li ◽  
Luc Nguyen
Keyword(s):  
Ricci Curvature ◽  
Compactness Theorem ◽  
Yamabe Problem ◽  
Fully Nonlinear ◽  
Curvature Bound

scholarly journals Comparison Geometry of Manifolds with Boundary under a Lower Weighted Ricci Curvature Bound

2018 ◽  
Vol 72 (1) ◽  
pp. 243-280
Author(s):  
Yohei Sakurai
Keyword(s):  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Suitable Condition ◽  
Manifolds With Boundary ◽  
Weighted Mean ◽  
Curvature Condition ◽  
Curvature Bound ◽  
Comparison Geometry ◽  
Weighted Mean Curvature ◽  
Weighted Ricci Curvature

AbstractWe study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition and a suitable condition for the weighted mean curvature for the boundary, we obtain various comparison geometric results.

scholarly journals Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound

2016 ◽  
Vol 6 (4) ◽  
pp. 807-835 ◽  
Author(s):  
Asma Hassannezhad ◽  
Gerasim Kokarev ◽  
Iosif Polterovich
Keyword(s):  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Curvature Bound
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