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We prove stability estimates for the Brunn-Minkowski inequality for convex sets.
Bobkov, S.G., Isoperimetric and analytic inequalities for log-concave probability measures
1921
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Knothe, H., Contributions to the theory of convex bodies
1957
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Borell, C., Complements of Lyapunov’s inequality
1973
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Diskant, V. I., Stability of the Solution of the Minkowski Equation
1973
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Osserman, R., Bonnesen-style isoperimetric inequalities
1979
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Groemer, H., On the Brunn�-Minkowski theorem
1988
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Milman, V. D., Pajor, A., Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n n -dimensional space
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Pisier, G., The volume of convex bodies and Banach space geometry
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Bourgain, J., On the distribution of polynomials on high-dimensional convex sets
1991
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Bobkov, S.G., Extremal properties of half-spaces for log-concave distributions
1996
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Bobkov, S.G., On coccentration of distributions of random weighted sums
2003
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Nazarov, F., Sodin, M., Volberg, A., The geometric Kannan-Lovász-Simonovits lemma, dimension-free estimates for the distribution of the values of polynomials, and the distribution of the zeros of random analytic functions
2003
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Villani, C., Topics in optimal transportation
2003
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Klartag, B., A central limit theorem for convex sets
2007
Eldan, R., Klartag, B., Pointwise estimates for marginals of convex bodies
2008
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Carlier, G., Galichon, A., Santambrogio, F., From Knothe’s Transport to Brenier’s Map and a Continuation Method for Optimal Transport
2009
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Figalli, A., Maggi, F., Pratelli, A., A refined Brunn-Minkowski inequality for convex sets
2009
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Klartag, B., A Berry-Esseen type inequality for convex bodies with an unconditional basis
2009
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Figalli, A., Maggi, F., Pratelli, A., A mass transportation approach to quantitative isoperimetric inequalities
2010
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Ball, K. M., Böröczky, K. J., Stability of some versions of the PrékopaLeindler inequality
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Cited alongside, same era.
Lovász, L., Vempala, S., The geometry of logconcave functions and sampling algorithms
2007
Cited alongside, same era.
2011
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Eldan, R., Klartag, B., Approximately Gaussian marginals and the hyperplane conjecture
2011
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