A refined Brunn-Minkowski inequality for convex sets

By Alessio Figalli, Francesco Maggi, Aldo Pratelli. 2009

122 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/00cd69a58f451719d7c653381614f49ed62dd36a

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In Applied Mathematics

Citations in the corpus

A Sharp Stability Result for the Relative Isoperimetric Inequality Inside Convex Cones (2012, background): “Their proof is based on the Brunn-Minkowski inequality which states that if A,B ⊂ Rn are measurable, then |A+B| 1 n ≥ |A| 1 n + |B| 1 n .”
Stability of some versions of the Prékopa–Leindler inequality (2009, background): “Recently Figalli et al. [ 13 ,14] obtained an optimal stability version of the Brunn-”
Local $L^p$-Brunn-Minkowski inequalities for $p<1$ (2017, methodology): “All the proofs in [18, 61, 29] employ the following so-called “Poincaré-type trace inequality” proved by Figalli–Maggi–Pratelli in [18].”
New approach to the affine P\'olya-Szeg\"o principle and the stability version of the affine Sobolev inequality (2015, background): “We refer the reader to [2, 3, 4, 5, 10, 11, 12, 19, 21, 22, 23, 24, 25, 26] and references therein for more background and results in this direction.”
Transport Inequalities for Log-concave Measures, Quantitative Forms, and Applications (2015, background): “Mass transport arguments combinedwith Poincaré inequalities (of a diòerent nature than the one we use) were put forward to exhibit remainder terms in isoperimetric type inequalities in the far-reaching work of Figalli, Maggi, and Pratelli, in particular in [15] for the case of log-concave measures (”
A Selection Principle for the Sharp Quantitative Isoperimetric Inequality (2010, background): “Since the publication of [19] the study of quantitative forms of various geometric and functional inequalities has received a new impulse (see for instance [8,13,14,18,20] and the review paper [26]).”
Quantitative stability for sumsets in $R^n$ (2014, methodology): “Furthermore, if we restrict A and B to the class of convex sets, a quantitative stability estimate for the Brunn-Minkowski inequality, with the sharp power law dependence on the deficit, was proved in [6, 7].”
Quantitative logarithmic Sobolev inequalities and stability estimates (2014, result): “Examples of such results are the recent quantitative stability estimates for Sobolev [12, 19], Brunn-Minkowski [17, 16], and isoperimetric inequalities [20, 18, 15, 23].”
Dar’s conjecture and the log–Brunn–Minkowski inequality (2016, background): “Figalli, Maggi, and Pratelli [13,14] tackled the stability problem for convex bodies with a more natural distance, i.e., “relative asymmetry” (which has a close relationship with the functionalM(K,L)), by using mass transportation approach.”
Sharp gradient stability for the Sobolev inequality (2020, background): “Introduction Motivated by important applications to problems in the calculus of variations and evolution PDEs, in recent years there has been a growing interest around the understanding of quantitative stability for functional/geometric inequalities, see for instance [3, 2, 8, 27, 28, 21, 9, 22, 29,”