Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
Citations
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Cites methods from "Generalization of an Inequality by ..."
...See e.g. [Ta95], [Le01], [BG99], [ OV00 ], [DD02], [CMS01], [AT04], [F¨...
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...for all 2 TM. An heuristic argument for the ’if’-implication of this equivalence was presented in [ OV00 ], based on the formal Riemannian calculus on P2(M)....
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1,357 citations
Cites background or methods from "Generalization of an Inequality by ..."
...Connections between optimal transport and the theory of log Sobolev inequalities and Poincaré inequalities were established by Otto and Villani [33] and developed by many authors, one notable contribution being that of Bobkov, Gentil and Ledoux [7]....
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...Otto and Villani [33] carried out Hessian computations for certain functions on P2(M) using a formal infinite-dimensional Riemannian structure on P2(M) defined by Otto [32]....
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...A formal differential calculus on P2(M), when M is a smooth Riemannian manifold, was described by Otto and Villani [36]....
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...Appendix D of the present paper follows up on the calculations in [36]....
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...Connections between optimal transport and the theory of log Sobolev inequalities and Poincaré inequalities were established by Otto and Villani [36] and developed by many authors....
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References
5,769 citations
"Generalization of an Inequality by ..." refers methods in this paper
...We refer to [13] for a proof of this and all the related facts that we shall use about second derivatives in the sense of Aleksandrov....
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1,780 citations
"Generalization of an Inequality by ..." refers result in this paper
...According to the results of Brenier [6], extended in McCann [23], there exists a (dμ0-a....
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...J.-D. Benamou and Y. Brenier, A numerical method for the optimal time-continuous mass transport problem and related problems, in ``Monge Ampe re Equation: Applications to Geometry and Optimization,'' Contemp....
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...Also this implies, by the Knott Smith Brenier characterization theorem, W(+0 , +t)=t | |{8|2 d+0 =tW(+0 , +1), 0 t 1....
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...Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Comm. Pure Appl....
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...According to the results of Brenier [6], extended in McCann [23], there exists a (d+0 -a.e) unique gradient of a convex function, {....
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"Generalization of an Inequality by ..." refers methods in this paper
...This formalism, which is somewhat reminiscent of Arnold’s [2] geometric viewpoint of fluid mechanics, was developed by the first author in [26]....
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1,552 citations