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We develop the optimal transportation approach to modified log-Sobolev inequalities and to isoperimetric inequalities.
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Lévy-Gromov’s isoperimetric inequality for an infinite-dimensional diffusion generator
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Transportation cost for Gaussian and other product measures
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Some connections between isoperimetric and Sobolev-type inequalities
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Rachev S.T. and Rüschendorf L., Mass transportation problems. V. I, II, Springer, New York, 1998
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Geometric asymptotics and the logarithmic Sobolev inequality
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Isoperimetric and analytic inequalities for log-concave probability measures
Bobkov S.G., · 1999
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Exponential integrability and transportation cost related to logarithmic Sobolev inequality
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From Brunn-Minkovsky to Brascamp-Lieb and to logarithmic Sobolev inequality
Bobkov S.G. and Ledoux M., · 2000
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Monotonicity properties of optimal transportation and the FKG and related inequalities
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The Santalo point of a function, and a functional form of Santalo inequality
Artstein S., Klartag B. and Milman V., · 2004
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Carlen E. and Loss M., Logarithmic Sobolev inequalities and spectral gaps., in Recent advances in the theory and applications of mass transport. — Contemp. Math. Amer. Math. Soc., v. 353, Providence, RI, 2004, p. 53–60
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Entropies, convexity, and functional inequalities: on Φ \Phi -entropies and Φ \Phi -Sobolev inequalities
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Inequalities for generalized entropies and optimal transportation
Cordero-Erausquin D., Gangbo W. and Houdré C., · 2004
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A mass-transportation approach to sharp Sobolev and Gagliardo–Nirenberg inequalities
Cordero-Erausquin D., Nazaret B. and Villani C., · 2004
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Latała R. and Oleskiewicz K., Between Sobolev and Poincaré. In Geometric aspects of functional analysis, Lecture Notes in Math., v. 1745, 2000, p. 147–168, Springer, Berlin
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Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
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Functional inequalities for empty essential spectrum
Wang F.-Y., · 2000
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Levels of concentration between exponential and Gaussian
Barthe F., · 2001
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Hypercontractivity of Hamilton–Jacobi equations
Bobkov S.G., Gentil I. and Ledoux M., · 2001
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A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
Cordero-Erausquin D., McCann R.J. and Schmuckenschläger M., · 2001
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Convexity inequalities and optimal transport of infinite-dimensional measures
Kolesnikov A.V., · 2004
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Gradient flows in metric spaces and in the space of probability measures
Ambrosio L., Gigli N. and Savaré G., · 2005
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Volume comparison theorems without Jacobi fields
Bakry D. and Qian Z., · 2005
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Bobkov S.G. and Zegarlinski B. Entropy bounds and isoperimetry. — Memoirs of the Amer. Math. Soc., v. 176, n. 829, 2005
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On the Monge–Ampère equation in infinite dimensions
Bogachev V.I. and Kolesnikov A.V., · 2005
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Hypercontractivity for perturbed diffusion semigroups
Cattiaux P., · 2005
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Modified logarithmic Sobolev inequalities and transportation inequalities
Gentil I., Guillin A., and Miclo L., · 2005
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The isoperimetric problem
Ros A., · 2005
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A generalization of Poincaré and log-Sobolev inequalities
Wang F.-Y., · 2005
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Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
Barthe F., Cattiaux P. and Roberto C., · 2006
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Prékopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport
Cordero-Erausquin D., McCann R.J. and Schmuckenschläger M., · 2006
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Markov chains in smooth Banach spaces and Gromov-hyperbolic metric spaces
Naor A., Peres Y., Schramm O. and Sheffield S., · 2006
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Orlicz-Poincaré inequalities. Preprint. 2006
Wang F.-Y., · 2006
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Modified logarithmic Sobolev inequalities in null curvature
Gentil I., Guillin A. and Miclo L., · 2007
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Modified log-Sobolev inequalities and isoperimetry
Kolesnikov A.V., · 2007
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Orlicz-Sobolev inequalities for sub-Gaussian measures and ergodicity of Markov semi-groups
Roberto C. and Zegarliński B., · 2007
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