Rigidity phenomena on lower N-weighted Ricci curvature bounds with ε-range for nonsymmetric Laplacian

2021 ◽  
Vol 65 (4) ◽  
Author(s):  
Kazuhiro Kuwae ◽  
Yohei Sakurai
Keyword(s):  
Ricci Curvature ◽  
Curvature Bounds ◽  
Weighted Ricci Curvature

scholarly journals Dilation Type Inequalities for Strongly-Convex Sets in Weighted Riemannian Manifolds

2021 ◽  
Vol 9 (1) ◽  
pp. 219-253
Author(s):  
Hiroshi Tsuji
Keyword(s):  
Ricci Curvature ◽  
Convex Sets ◽  
Convex Geometry ◽  
Type Inequality ◽  
Model Space ◽  
Functional Inequalities ◽  
Curvature Bounds ◽  
Strongly Convex ◽  
Weighted Ricci Curvature ◽  
The One

Abstract In this paper, we consider a dilation type inequality on a weighted Riemannian manifold, which is classically known as Borell’s lemma in high-dimensional convex geometry. We investigate the dilation type inequality as an isoperimetric type inequality by introducing the dilation profile and estimate it by the one for the corresponding model space under lower weighted Ricci curvature bounds. We also explore functional inequalities derived from the comparison of the dilation profiles under the nonnegative weighted Ricci curvature. In particular, we show several functional inequalities related to various entropies.

scholarly journals Smoothing Riemannian metrics with Ricci curvature bounds

1996 ◽  
Vol 90 (1) ◽  
pp. 49-61 ◽  
Author(s):  
Xianzhe Dai ◽  
Guofang Wei ◽  
Rugang Ye
Keyword(s):  
Ricci Curvature ◽  
Riemannian Metrics ◽  
Curvature Bounds
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