Prekopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport

By Dario Cordero-Erausquin, Robert J. McCann, M. Schmuckenschläger. 2006

79 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/4b7b7a929e92a654d7d9c7e9f62876f173b96d54

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In Applied Mathematics

Citations in the corpus

Poincaré and Brunn-Minkowski inequalities on the boundary of weighted Riemannian manifolds (2017, methodology): “Other more standard generalizations of the Brunn–Minkowski inequality in the weighted Riemannian setting and in the even more general metric-measure space setting, for spaces satisfying the CD(ρ,N) condition, have been obtained by Cordero-Erausquin–McCann–Schmuckenshläger [20, 21], Sturm [72], Lott–”
Beyond traditional Curvature-Dimension I: new model spaces for isoperimetric and concentration inequalities in negative dimension (2014, background): “also [52, 28, 15, 16, 55, 3, 56, 45, 40, 26] and the references therein), especially since Perelman’s work on the Poincaré Conjecture [51], and the extension of the Curvature-Dimension condition to the metric-measure space setting by Lott–Sturm–Villani [54, 33].”
Transport Inequalities. A Survey (2010, background): “It has been discovered by Barthe, CorderoErausquin, McCann, Nazaret and Villani, among others, that this is also true for other well-known functional inequalities such as Prékopa-Leindler, Brascamp-Lieb and Sobolev inequalities, see [5, 6, 29, 30, 41, 83].”
Finsler interpolation inequalities (2009, background): “Wefinallydiscusstheconcentrationofmeasurephenomenonalongthelinesof[18,Sect.1.6] (as well as [11, 12 ]).”
Ricci curvature for metric-measure spaces via optimal transport (2004, background): “In a more recent contribution, which was done independently of the present paper, Cordero-Erausquin, McCann and Schmuckenschl¨a ge r [20] prove the implication (1) ⇒ (5) of Theorem 7.3(b) for general �.”
On the role of convexity in isoperimetry, spectral gap and concentration (2007, background): “[24]) due to Cordero-Erausquin, McCann and Schmuckenschlager [ 29 ] (generalizing their own result from [28]).”
Five lectures on optimal transportation: Geometry, regularity and applications (2010, result): “One direction of this equivalence was proved by Cordero-Erausquin, McCann, and Schmuckenschäger [30] and Otto and Villani [110] in projects which were initially independent (see also [28] and [31]), while the converse was established by von Renesse and Sturm [116] confirming the formal arguments of ”
Mass Transport and Variants of the Logarithmic Sobolev Inequality (2007, methodology): “For more details about displacement convexity, abovetangent inequalities and applications, see [4, 34, 33, 37, 36, 2, 43, 28].”