29 citations · 30 across the 4 of their papers we have counts for
8 papers
Compact manifolds with fixed boundary and large Steklov eigenvalues
Bruno Colbois, Ahmad El Soufi, Alexandre Girouard
Let M be a compact Riemannian manifold with boundary. Let b>0 be the number of connected components of its boundary. For manifolds of dimension at least 3, we prove that it is poss…
On sums of eigenvalues of elliptic operators on manifolds
Ahmad El Soufi, Evans Harrell, Said Ilias +1
We use the averaged variational principle introduced in a recent article on graph spectra [7] to obtain upper bounds for sums of eigenvalues of several partial differential operato…
Extremal Eigenvalues of the Laplacian on Euclidean domains and closed surfaces
Bruno Colbois, Ahmad El Soufi
We investigate properties of the sequences of extremal values that could be achieved by the eigenvalues of the Laplacian on Euclidean domains of unit volume, under Dirichlet and Ne…
On the placement of an obstacle so as to optimize the Dirichlet heat trace
Ahmad El Soufi, Evans Harrell
We prove that among all doubly connected domains of bounded by two spheres of given radii, , the trace of the heat kernel with Dirichlet boundary conditions, achieves…
Eigenvalues of the Laplacian on a compact manifold with density
Bruno Colbois, Ahmad El Soufi, Alessandro Savo
In this paper, we study the spectrum of the weighted Laplacian (also called Bakry-Emery or Witten Laplacian) on a compact, connected, smooth Riemannian manifold endow…
Isoperimetric control of the Steklov spectrum
Bruno Colbois, Ahmad El Soufi, Alexandre Girouard
Let N be a complete Riemannian manifold of dimension n+1 whose Riemannian metric g is conformally equivalent to a metric with non-negative Ricci curvature. The normalized Steklov e…