Fetching the paper…
Reading the bibliography…
Various properties of isoperimetric, functional, Transport-Entropy and concentration inequalities are studied on a Riemannian manifold equipped with a measure, whose generalized Ricci curvature is bounded from below.
The negative spectrum of the higher-dimensional Schrödinger operator
V. G. Maz ′ · 1962
Earlier work this paper cites.
A lower bound for the smallest eigenvalue of the Laplacian
J. Cheeger · 1970
Earlier work this paper cites.
Hardy’s inequality with weights
B. Muckenhoupt · 1972
Earlier work this paper cites.
Logarithmic Sobolev inequalities
L. Gross · 1975
Earlier work this paper cites.
A note on the isoperimetric constant
P. Buser · 1982
Earlier work this paper cites.
A topological application of the isoperimetric inequality
M. Gromov and V. D. Milman · 1983
Earlier work this paper cites.
Diffusions hypercontractives
D. Bakry and M. Émery · 1985
Earlier work this paper cites.
Sobolev spaces
V. G. Maz ′ · 1985
Earlier work this paper cites.
A simple proof of the blowing-up lemma
K. Marton · 1986
Earlier work this paper cites.
Logarithmic Sobolev inequalities and stochastic Ising models
R. Holley and D. Stroock · 1987
Earlier work this paper cites.
The heritage of P. Lévy in geometrical functional analysis
V. D. Milman · 1987
Earlier work this paper cites.
The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition
D. W. Stroock and B. Zegarliński · 1992
Earlier work this paper cites.
A simple analytic proof of an inequality by P. Buser
M. Ledoux · 1994
Earlier work this paper cites.
Lévy-Gromov’s isoperimetric inequality for an infinite-dimensional diffusion generator
D. Bakry and M. Ledoux · 1996
Earlier work this paper cites.
Extremal properties of half-spaces for log-concave distributions
S. Bobkov · 1996
Earlier work this paper cites.
Bounding d ¯ \overline{d} -distance by informational divergence: a method to prove measure concentration
K. Marton · 1996
Earlier work this paper cites.
Transportation cost for Gaussian and other product measures
M. Talagrand · 1996
Earlier work this paper cites.
An isoperimetric inequality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space
S. G. Bobkov · 1997
Earlier work this paper cites.
Isoperimetric constants for product probability measures
S. G. Bobkov and C. Houdré · 1997
Earlier work this paper cites.
Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution
S. G. Bobkov and M. Ledoux · 1997
Earlier work this paper cites.
Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
F.-Y. Wang · 1997
Cited alongside, same era.
Isoperimetric and analytic inequalities for log-concave probability measures
S. G. Bobkov · 1999
Cited alongside, same era.
Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
S. G. Bobkov and F. Götze · 1999
Cited alongside, same era.
Correlations, spectral gap and log-Sobolev inequalities for unbounded spins systems
T. Bodineau and B. Helffer · 2000
Cited alongside, same era.
The geometry of Markov diffusion generators
M. Ledoux · 2000
Cited alongside, same era.
Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
F. Otto and C. Villani · 2000
Cited alongside, same era.
Characterization of Talagrand’s like transportation-cost inequalities on the real line
N. Gozlan · 2007
Later among the works it cites.
A large deviation approach to some transportation cost inequalities
N. Gozlan and C. Léonard · 2007
Later among the works it cites.
Modified log-Sobolev inequalities and isoperimetry
A. V. Kolesnikov · 2007
Later among the works it cites.
Hamilton-Jacobi semigroup on length spaces and applications
J. Lott and C. Villani · 2007
Later among the works it cites.
Mass transport and variants of the logarithmic Sobolev inequality
F. Barthe and A. V. Kolesnikov · 2008
Later among the works it cites.
Modified logarithmic Sobolev inequalities on ℝ \mathbb{R}
F. Barthe and C. Roberto · 2008
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Levels of concentration between exponential and Gaussian
F. Barthe · 2001
Cited alongside, same era.
Hypercontractivity of Hamilton-Jacobi equations
S. G. Bobkov, I. Gentil, and M. Ledoux · 2001
Cited alongside, same era.
The concentration of measure phenomenon
M. Ledoux · 2001
Cited alongside, same era.
Logarithmic Sobolev inequalities: conditions and counterexamples
F.-Y. Wang · 2001
Cited alongside, same era.
The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice
N. Yoshida · 2001
Cited alongside, same era.
Transportation cost-information inequalities and applications to random dynamical systems and diffusions
H. Djellout, A. Guillin, and L. Wu · 2004
Cited alongside, same era.
Uniform tail-decay of Lipschitz functions implies Cheeger ′
E. Milman · 2008
Later among the works it cites.
An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies
E. Milman and S. Sodin · 2008
Later among the works it cites.
From super Poincaré to weighted log-Sobolev and entropy-cost inequalities
F.-Y. Wang · 2008
Later among the works it cites.
Functional inequalities and hamilton-jacobi equations in geodesic spaces
Z. M. Balogh, A. Engoulatov, L. Hunziker, and O. E. Maasalo · 2009
Closest in time.
A characterization of dimension free concentration in terms of transportation inequalities
N. Gozlan · 2009
Closest in time.
From concentration to isoperimetry: Semigroup proofs
M. Ledoux · 2009
Closest in time.
Concentration and isoperimetry are equivalent assuming curvature lower bound
E. Milman · 2009
Closest in time.
Isoperimetric and concentration inequalities - equivalence under curvature lower bound
E. Milman · 2009
Closest in time.
On the role of convexity in functional and isoperimetric inequalities
E. Milman · 2009
Closest in time.
On the role of convexity in isoperimetry, spectral-gap and concentration
E. Milman · 2009
Closest in time.
Optimal transport - old and new
C. Villani · 2009
Closest in time.
A new characterization of talagrand’s transport-entropy inequalities and applications
N. Gozlan, C. Roberto, and P.-M. Samson · 2010
Closest in time.
A converse to the Maz’ya inequality for capacities under curvature lower bound
E. Milman · 2010
Closest in time.