Add to ORKGOn a generic metric measured space, we introduce a notion of improved concentration of measure that takes into account the parallel enlargement of k distinct sets. We show that the k-th eigenvalues of the metric Laplacian gives exponential improved concentration with k sets. On compact Riemannian manifolds, this allows us to recover estimates on the eigenvalues of the Laplace-Beltrami operator in the spirit of an inequality of Chung, Grigor’yan & Yau, Upper bounds for eigenvalues of the discrete and continuous Laplace operators. Adv. Math. 117(2), 165–178 (1996)
Abstract. In this article we examine the concentration and oscillation effects developed by high-fre...
Given an open set $\Omega$, we consider the problem of providing sharp lower bounds for $\lambda_2(...
LaTeX, 11 pagesThe known upper bounds for the multiplicities of the Laplace-Beltrami operator eigenv...
peer reviewedOn a generic metric measured space, we introduce a notion of improved concentration of...
On a generic metric measured space, we introduce a notion of improved concentration of measure that ...
Let M(n) = (M, g) be a compact, connected, Riemannian manifold of dimension n. Let mu be the measure...
In this paper, we are concerned with upper bounds of eigenvalues of Laplace operator on compact Riem...
The concentration properties of eigenfunctions of the Laplace-Beltrami operator are closely linked t...
We use the averaged variational principle introduced in a recent article on graph spectra [10] to ob...
In this thesis, we give a review of known results concerning the concentration of Laplace eigenfunct...
In this paper, we develop a universal approach for estimating from above the eigenvalues of the Lapl...
We obtain various lower and upper estimates for the first eigenvalue of Dirichlet Laplacians defined...
We prove a lower bound for the k-th Steklov eigenvalues in terms of an isoperimetric constant called...
We prove inequalities for Laplace eigenvalues on Riemannian manifolds generalising to higher eigenva...
To appear, London Math SocietyInternational audienceWe give upper bounds for the eigenvalues of the ...
Abstract. In this article we examine the concentration and oscillation effects developed by high-fre...
Given an open set $\Omega$, we consider the problem of providing sharp lower bounds for $\lambda_2(...
LaTeX, 11 pagesThe known upper bounds for the multiplicities of the Laplace-Beltrami operator eigenv...
peer reviewedOn a generic metric measured space, we introduce a notion of improved concentration of...
On a generic metric measured space, we introduce a notion of improved concentration of measure that ...
Let M(n) = (M, g) be a compact, connected, Riemannian manifold of dimension n. Let mu be the measure...
In this paper, we are concerned with upper bounds of eigenvalues of Laplace operator on compact Riem...
The concentration properties of eigenfunctions of the Laplace-Beltrami operator are closely linked t...
We use the averaged variational principle introduced in a recent article on graph spectra [10] to ob...
In this thesis, we give a review of known results concerning the concentration of Laplace eigenfunct...
In this paper, we develop a universal approach for estimating from above the eigenvalues of the Lapl...
We obtain various lower and upper estimates for the first eigenvalue of Dirichlet Laplacians defined...
We prove a lower bound for the k-th Steklov eigenvalues in terms of an isoperimetric constant called...
We prove inequalities for Laplace eigenvalues on Riemannian manifolds generalising to higher eigenva...
To appear, London Math SocietyInternational audienceWe give upper bounds for the eigenvalues of the ...
Abstract. In this article we examine the concentration and oscillation effects developed by high-fre...
Given an open set $\Omega$, we consider the problem of providing sharp lower bounds for $\lambda_2(...
LaTeX, 11 pagesThe known upper bounds for the multiplicities of the Laplace-Beltrami operator eigenv...