scholarly journals Characterization of Pinched Ricci Curvature by Functional Inequalities

2017 ◽  
Vol 28 (3) ◽  
pp. 2312-2345 ◽  
Author(s):  
Li-Juan Cheng ◽  
Anton Thalmaier
Keyword(s):  
Ricci Curvature ◽  
Functional Inequalities

scholarly journals A pair of linear functional inequalities and a characterization of Lp-norm

2005 ◽  
Vol 85 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Dorota Krassowska ◽  
Janusz Matkowski
Keyword(s):  
Linear Functional ◽  
Functional Inequalities ◽  
Lp Norm

Almost Ricci solitons isometric to spheres

2019 ◽  
Vol 16 (05) ◽  
pp. 1950073 ◽  
Author(s):  
Sharief Deshmukh
Keyword(s):  
Lower Bound ◽  
Poisson Equation ◽  
Ricci Curvature ◽  
Unit Sphere ◽  
Potential Field ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Almost Ricci Soliton

We find a characterization of a sphere using a compact gradient almost Ricci soliton and the lower bound on the integral of Ricci curvature in the direction of potential field. Also, we use Poisson equation on a compact gradient almost Ricci soliton to find a characterization of the unit sphere.

Constructions of Einstein Finsler metrics by warped product

2018 ◽  
Vol 29 (11) ◽  
pp. 1850081 ◽  
Author(s):  
Bin Chen ◽  
Zhongmin Shen ◽  
Lili Zhao
Keyword(s):  
Ricci Curvature ◽  
Warped Product ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Product Structures

The warped product structures of Finsler metrics are studied in this paper. We give the formulae of the flag curvature and Ricci curvature of these metrics, and obtain the characterization of such metrics to be Einstein. Some Einstein Finsler metrics of this type are constructed.

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.

ON THE COMPACTNESS OF MANIFOLDS

2003 ◽  
Vol 06 (supp01) ◽  
pp. 29-38 ◽  
Author(s):  
XUE-MEI LI ◽  
FENG-YU WANG
Keyword(s):  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Positive Constant ◽  
Riemannian Metric ◽  
Sobolev Inequalities ◽  
Functional Inequalities ◽  
The Family ◽  
Bounded Below

It is believed that the family of Riemannian manifolds with negative curvatures is much richer than that with positive curvatures. In fact there are many results on the obstruction of furnishing a manifold with a Riemannian metric whose curvature is positive. In particular any manifold admitting a Riemannian metric whose Ricci curvature is bounded below by a positive constant must be compact. Here we investigate such obstructions in terms of certain functional inequalities which can be considered as generalized Poincaré or log-Sobolev inequalities. A result of Saloff-Coste is extended.

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