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It is well known that isoperimetric inequalities imply in a very general measure-metric-space setting appropriate concentration inequalities.
Minimal cones and the Bernstein problem
E. Bombieri, E. De Giorgi, and E. Giusti · 1969
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H. Federer · 1969
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Extremal properties of half-spaces for spherically invariant measures
V. N. Sudakov and B. S. Cirel ′ · 1974
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Ch. Borell · 1975
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E. Heintze and H. Karcher · 1978
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Paul Lévy’s isoperimetric inequality
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A note on the isoperimetric constant
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Minimal surfaces and functions of bounded variation
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Diffusions hypercontractives
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Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov
P. Bérard, G. Besson, and S. Gallot · 1985
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Sur le volume minimal de ℝ 2 \mathbb{R}^{2}
C. Bavard and P. Pansu · 1986
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Éléments extrémaux pour les inégalités de Brunn-Minkowski gaussiennes
A. Ehrhard · 1986
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Inégalités isopérimétriques et analytiques sur les variétés riemanniennes
S. Gallot · 1986
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Boundary regularity for solutions of a partitioning problem
M. Grüter · 1987
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The heritage of P. Lévy in geometrical functional analysis
V. D. Milman · 1987
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Geometric inequalities
Yu. D. Burago and V. A. Zalgaller · 1988
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Lévy-Gromov’s isoperimetric inequality for an infinite-dimensional diffusion generator
D. Bakry and M. Ledoux · 1996
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Extremal properties of half-spaces for log-concave distributions
S. Bobkov · 1996
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A functional form of the isoperimetric inequality for the Gaussian measure
S. G. Bobkov · 1996
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Logarithmic Sobolev inequalities, Poincaré inequalities and heat kernel bounds
D. Bakry, M. Ledoux, and Z. Qian · 1997
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Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
F.-Y. Wang · 1997
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Isoperimetric and analytic inequalities for log-concave probability measures
S. G. Bobkov · 1999
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Propriétés de concavité du profil isopérimétrique et applications
V. Bayle · 2004
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Riemannian geometry
S. Gallot, D. Hulin, and J. Lafontaine · 2004
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Spectral gap, logarithmic Sobolev constant, and geometric bounds
M. Ledoux · 2004
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Some isoperimetric comparison theorems for convex bodies in Riemannian manifolds
V. Bayle and C. Rosales · 2005
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Manifolds with density
F. Morgan · 2005
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Isoperimetric regions in spaces
M. Lee · 2006
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Optimal integrability condition for the log-Sobolev inequality
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Metric structures for Riemannian and non-Riemannian spaces
M. Gromov · 1999
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On the connectivity of boundaries of sets minimizing perimeter subject to a volume constraint
P. Sternberg and K. Zumbrun · 1999
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Some sharp isoperimetric theorems for Riemannian manifolds
F. Morgan and D. L. Johnson · 2000
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Levels of concentration between exponential and Gaussian
F. Barthe · 2001
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On the cases of equality in Bobkov’s inequality and Gaussian rearrangement
E. A. Carlen and C. Kerce · 2001
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The concentration of measure phenomenon
M. Ledoux · 2001
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X. Chen and F.-Y. Wang · 2007
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Mass transport and variants of the logarithmic Sobolev inequality
F. Barthe and A. V. Kolesnikov · 2008
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Uniform tail-decay of Lipschitz functions implies Cheeger ′
E. Milman · 2008
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An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies
E. Milman and S. Sodin · 2008
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On the role of convexity in functional and isoperimetric inequalities
E. Milman · 2009
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On the role of convexity in isoperimetry, spectral-gap and concentration
E. Milman · 2009
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Concentration and isoperimetry are equivalent assuming curvature lower bound
E. Milman · 2009
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Properties of Isoperimetric, Functional and Transport-Entropy Inequalities Via Concentration
E. Milman · 2009
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Optimal isoperimetric, log-Sobolev and spectral gap inequalities on compact manifolds with density
E. Milman · 2009
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Geometric measure theory
F. Morgan · 2009
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