Aspects of comparison geometry

2006 ◽  
pp. 157-181
Author(s):  
Karsten Grove
Keyword(s):  
Comparison Geometry

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.

Comparison Geometry With L1-Norms of Ricci Curvature

2006 ◽  
Vol 49 (1) ◽  
pp. 152-160
Author(s):  
Jong-Gug Yun
Keyword(s):  
Ricci Curvature ◽  
Comparison Theorem ◽  
Sphere Theorem ◽  
Volume Comparison ◽  
Comparison Geometry

AbstractWe investigate the geometry of manifolds with bounded Ricci curvature in L1-sense. In particular, we generalize the classical volume comparison theorem to our situation and obtain a generalized sphere theorem.

Comparison Geometry with Integral Curvature Bounds

1997 ◽  
Vol 7 (6) ◽  
pp. 1011-1030 ◽  
Author(s):  
P. Peterson ◽  
S.D. Shteingold ◽  
G. Wei
Keyword(s):  
Integral Curvature ◽  
Curvature Bounds ◽  
Comparison Geometry

scholarly journals Comparison geometry for the Bakry-Emery Ricci tensor

2009 ◽  
Vol 83 (2) ◽  
pp. 337-405 ◽  
Author(s):  
Guofang Wei ◽  
Will Wylie
Keyword(s):  
Ricci Tensor ◽  
Comparison Geometry

scholarly journals Paolo Pizzetti: The forgotten originator of triangle comparison geometry

2011 ◽  
Vol 38 (3) ◽  
pp. 415-422 ◽  
Author(s):  
Victor Pambuccian ◽  
Tudor Zamfirescu
Keyword(s):  
Comparison Geometry

scholarly journals Comparison geometry referred to warped product models

2006 ◽  
Vol 58 (4) ◽  
pp. 461-473 ◽  
Author(s):  
Yukihiro Mashiko ◽  
Katsuhiro Shiohama
Keyword(s):  
Warped Product ◽  
Comparison Geometry ◽  
Product Models
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