75 citations · 105 across the 14 of their papers we have counts for
7 papers · 1 filter
Universal inequalities for the eigenvalues of Schrodinger operators on submanifolds
Ahmad El Soufi, Evans Harrell, Said Ilias
We establish inequalities for the eigenvalues of Schrödinger operators on compact submanifolds (possibly with nonempty boundary) of Euclidean spaces, of spheres, and of real, compl…
Where to place a spherical obstacle so as to maximize the second Dirichlet eigenvalue
Ahmad El Soufi, Rola Kiwan
We prove that among all doubly connected domains of bounded by two spheres of given radii, the second eigenvalue of the Dirichlet Laplacian achieves its maximum when…
Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold
Ahmad El Soufi, Saïd Ilias
For any bounded regular domain of a real analytic Riemannian manifold , we denote by the -th eigenvalue of the Dirichlet Laplacian of . In this paper, we co…
Laplacian eigenvalues functionals and metric deformations on compact manifolds
Ahmad El Soufi, Said Ilias
In this paper, we investigate critical points of the Laplacian's eigenvalues considered as functionals on the space of Riemmannian metrics or a conformal class of metrics on a comp…
A unique extremal metric for the least eigenvalue of the Laplacian on the Klein bottle
Ahmad El Soufi, Hector Giacomini, Mustapha Jazar
We prove the following conjecture recently formulated by Jakobson, Nadirashvili and Polterovich \cite{JNP}: on the Klein bottle , the metric of revolution $$g_0= {9+ (1…
Greatest least eigenvalue of the Laplacian on the Klein bottle
Ahmad El Soufi, Hector Giacomini, Mustapha Jazar
We prove the following conjecture recently formulated by Jakobson, Nadirashvili and Polterovich \cite{JNP}: For any Riemannian metric on the Klein bottle one has $…