A Toponogov-Type Comparison Theorem for Finsler Manifolds and its Applications

2019 ◽  
Vol 45 (5) ◽  
pp. 1531-1543
Author(s):  
Bing-Ye Wu
Keyword(s):  
Comparison Theorem ◽  
Finsler Manifolds

scholarly journals On interpolation and curvature via Wasserstein geodesics

2017 ◽  
Vol 10 (2) ◽  
pp. 125-167 ◽  
Author(s):  
Martin Kell
Keyword(s):  
Ricci Curvature ◽  
Comparison Theorem ◽  
Similar Condition ◽  
Interpolation Inequality ◽  
Metric Measure Spaces ◽  
Main Ingredient ◽  
Curvature Condition ◽  
Finsler Manifolds ◽  
Measure Spaces ◽  
Positively Curved

AbstractIn this article, a proof of the interpolation inequality along geodesics in p-Wasserstein spaces is given. This interpolation inequality was the main ingredient to prove the Borel–Brascamp–Lieb inequality for general Riemannian and Finsler manifolds and led Lott–Villani and Sturm to define an abstract Ricci curvature condition. Following their ideas, a similar condition can be defined and for positively curved spaces one can prove a Poincaré inequality. Using Gigli’s recently developed calculus on metric measure spaces, even a q-Laplacian comparison theorem holds on q-infinitesimal convex spaces. In the appendix, the theory of Orlicz–Wasserstein spaces is developed and necessary adjustments to prove the interpolation inequality along geodesics in those spaces are given.

A Universal Volume Comparison Theorem for Finsler Manifolds and Related Results

2013 ◽  
Vol 65 (6) ◽  
pp. 1401-1435 ◽  
Author(s):  
Wei Zhao ◽  
Yibing Shen
Keyword(s):  
Isoperimetric Inequality ◽  
Comparison Theorem ◽  
Finsler Geometry ◽  
Finsler Manifolds ◽  
Volume Comparison

AbstractIn this paper, we establish a universal volume comparison theorem for Finsler manifolds and give the Berger–Kazdan inequality and Santalá's formula in Finsler geometry. Based on these, we derive a Berger–Kazdan type comparison theorem and a Croke type isoperimetric inequality for Finsler manifolds.

ON INTEGRAL RICCI CURVATURE AND TOPOLOGY OF FINSLER MANIFOLDS

2012 ◽  
Vol 23 (11) ◽  
pp. 1250111 ◽  
Author(s):  
B. Y. WU
Keyword(s):  
Ricci Curvature ◽  
Comparison Theorem ◽  
Relative Volume ◽  
Volume Form ◽  
Finsler Manifolds ◽  
Volume Comparison ◽  
Minimal Volume ◽  
Curvature Bound ◽  
And Topology

We establish a relative volume comparison theorem for minimal volume form of Finsler manifolds under integral Ricci curvature bound. As its applications, we obtain some results on integral Ricci curvature and topology of Finsler manifolds. These results generalize the corresponding properties with pointwise Ricci curvature bound in the literatures.

scholarly journals Sufficient Criteria for Obtaining Hardy Inequalities on Finsler Manifolds

2021 ◽  
Vol 18 (2) ◽  
Author(s):  
Ágnes Mester ◽  
Ioan Radu Peter ◽  
Csaba Varga
Keyword(s):  
Finsler Manifolds ◽  
Hardy Inequalities

scholarly journals A comparison theorem

1985 ◽  
Vol 106 (1) ◽  
pp. 188-195
Author(s):  
Walter Leighton
Keyword(s):  
Comparison Theorem

scholarly journals A representation theorem for the linear quasi-differential equation(py′)′+qy=0

2000 ◽  
Vol 23 (8) ◽  
pp. 579-584
Author(s):  
J. G. O'Hara
Keyword(s):  
Differential Equation ◽  
Comparison Theorem ◽  
Simple Proof ◽  
Representation Theorem ◽  
Second Order ◽  
Order Linear

We establish a representation forqin the second-order linear quasi-differential equation(py′)′+qy=0. We give a number of applications, including a simple proof of Sturm's comparison theorem.

scholarly journals Cohomological comparison theorem

2015 ◽  
Vol 219 (12) ◽  
pp. 5573-5589
Author(s):  
Edward L. Green ◽  
Dag Oskar Madsen ◽  
Eduardo Marcos
Keyword(s):  
Comparison Theorem
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