The (B) conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems

By Dario Cordero-Erausquin, Matthieu Fradelizi, B. Maurey. 2004

132 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/de6cb0f412153161e45f283bbe3dc872d495edd0

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In Applied Mathematics

Citations in the corpus

On the stability of Brunn–Minkowski type inequalities (2016, background): “The latter is indeed true: it follows from the results of [11] and [23].”
Small ball probability estimates for log-concave measures (2012, background): “2 makes use of the affirmative answer to the B-conjecture by Cordero-Erausquin, Fradelizi and Maurey (see [5]).”
Small ball probability and Dvoretzky’s Theorem (2004, methodology): “It was recently deduced by R. Lata la and K. Oleszkiewicz [LO] from the B-conjecture proved by Cordero, Fradelizi and Maurey [ CFM ].”
More on logarithmic sums of convex bodies (2014, methodology): “Moreover, the following fact, also from [9], will be used: Theorem C.”
A note on a Brunn-Minkowski inequality for the Gaussian measure (2012, background): “n + (1 −λ)γn(B)1/n? A counter-example is given in this note. However, we believe that this question has an aﬃrmative answer in the case of o-symmetric convex sets, i.e. the sets satisfying K = −K. In [CFM] it is proved that for an o-symmetric convex set K in Rn the function (1) R∋ t → γn(etK), is lo”
Local Lp-Brunn-Minkowski inequalities for p<1 (2017, background): “valent to the conjecture that: λ1,e(−LK) ≥ n−p n−1 ( > 1). (1.7) In other words, it is a “next eigenvalue” conjecture (similar in spirit to the Bconjecture for the Gaussian measure, established in [16]). This elucidates the requirement that K be origin-symmetric, since then even functions are aut”
On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric-type inequalities (2015, background): “Moreover, in [8] (Proposition 8, see also Proposition 4.”
Some functional forms of Blaschke–Santaló inequality (2006, methodology): “The Prékopa–Leindler inequality for the geometric mean was also used in [8] to prove that if K is an unconditional convex body and μ has an unconditional log-concave density with respect to the Lebesgue measure, then t ,→ μ(etK) is a log-concave function.”
The dimensional Brunn–Minkowski inequality in Gauss space (2020, methodology): “In order to prove (8), Cordero-Erausquin, Fradelizi and Maurey succeeded to realize this inequality as special case of a second eigenvalue problem for even functions and then crucially used the symmetry of both the measure γ K and the function x (cid:55)→ | x | 2 .”
Local $L^p$-Brunn-Minkowski inequalities for $p<1$ (2017, background): “In other words, it is a “next eigenvalue” conjecture (similar in spirit to the Bconjecture for the Gaussian measure, established in [16]).”
A Berry-Esseen type inequality for convex bodies with an unconditional basis (2007, background): “Cordero-Erausquin, Fradelizi and Maurey [12] have recently proved the socalled (B)-conjecture in the unconditional case.”
Gaussian Brunn-Minkowski inequalities (2010, background): “As was mentioned above, the (B) conjecture was proved by Cordero-Erasquin, Fradelizi, and Maurey [10].”
A generalization of Caffarelli’s contraction theorem via (reverse) heat flow (2010, unknown): “14], Caﬀarelli’s Contraction Theorem has found numerous applications in various ﬁelds, serving as a tool to transfer isoperimetric inequalities, obtaining correlation inequalities, and more (see e.g. [17, 18, 26, 33]). Most of these applications only use the fact that there exists some contracting m”
Bourgain’s slicing problem and KLS isoperimetry up to polylog (2022, methodology): “However, according to Cordero-Erausquin, Fradelizi and Maurey [16, Lemma 2], under the 1-uniform log-concavity assumption, functions whose gradient is centered satisfy the Poincaré inequality with constant 12 (rather than 1).”