• Corpus ID: 125799742

Éléments extrémaux pour les inégalités de Brunn-Minkowski gaussiennes

@article{Ehrhard1986lmentsEP,
  title={{\'E}l{\'e}ments extr{\'e}maux pour les in{\'e}galit{\'e}s de Brunn-Minkowski gaussiennes},
  author={Antoine Ehrhard},
  journal={Annales De L Institut Henri Poincare-probabilites Et Statistiques},
  year={1986},
  volume={22},
  pages={149-168}
}
  • A. Ehrhard
  • Published 1986
  • Mathematics
  • Annales De L Institut Henri Poincare-probabilites Et Statistiques
On etudie les ensembles pour lesquels l'egalite est atteinte dans les inegalites de C. Borell et de Brunn-Minkowski gaussienne en dimension finie. On caracterise aussi les fonctions telles que l'inegalite isoperimetrique d'Ehrhard (1984) se reduit a une egalite 
archive.numdam.org
44 Citations
Highly Influential Citations
3
Background Citations
16
Methods Citations
3

44 Citations

The Brunn-Minkowski inequality
In 1978, Osserman [124] wrote an extensive survey on the isoperimetric inequality. The Brunn-Minkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality…
Gaussian Brunn-Minkowski inequalities
A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality is proved, together with precise equality conditions, and…
The equality cases of the Ehrhard–Borell inequality
On the isoperimetric problem in Euclidean space with density
We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we…
On isoperimetric inequalities with respect to infinite measures
We study isoperimetric problems with respect to infinite measures on $R ^n$. In the case of the measure $\mu$ defined by $d\mu = e^{c|x|^2} dx$, $c\geq 0$, we prove that, among all sets with given…
LINEAR ELLIPTIC EQUATIONS AND GAUSS MEASURE
In this paper we study a Dirichlet problem relative to a linear elliptic equation with lower-order terms, whose ellipticity condition is given in terms of the function φ(x)= (2π)− n 2 exp(−|x|/2) ,…
ON THE ISOPERIMETRIC DEFICIT IN GAUSS
We prove a sharp quantitative version of the isoperimetric inequality in the space Rn endowed with the Gaussian measure.
A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures
We show that for any log-concave measure μ on R, any pair of symmetric convex sets K and L, and any λ ∈ [0, 1], μ((1 − λ)K + λL) ≥ (1 − λ)μ(K) + λμ(L) , where cn ≥ n. This constitutes progress…
Essential connectedness and the rigidity problem for Gaussian symmetrization
We provide a geometric characterization of rigidity of equality cases in Ehrhard's symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new measure-theoretic…
An optimal Poincaré-Wirtinger inequality in Gauss space
Let $\Omega$ be a smooth, convex, unbounded domain of $\R^N$. Denote by $\mu_1(\Omega)$ the first nontrivial Neumann eigenvalue of the Hermite operator in $\Omega$; we prove that $\mu_1(\Omega) \ge…
...
...

References

SHOWING 1-9 OF 9 REFERENCES
Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes
© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1984, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.…
Symétrisation dans l'espace de Gauss.
The Brunn-Minkowski inequality in Gauss space
Espaces vectoriels topologiques
nnales de l'Institut Henri Poincaré -Probabilités et Statistiques
    V = BT x t2 [, et pour tout 0, 1, 2 }, xi = (zi, 0) ; les éléments F, xo, xi, x2, I et V
    • On pose alors m = n + 1, F = A( f )
    COROLLAIRE. -Soit f une fonction lipschitzienne de vers f~8
      0, alors f garde un signe constant sur [Rn et il existe un vecteur unitaire w de f~n tel que
        Eu(F)). Cela montre que Om{A(f)) &#x3E