29 citations · 149 across the 40 of their papers we have counts for
7 papers · 1 filter
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…
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…
Two properties of volume growth entropy in Hilbert geometry
Bruno Colbois, Patrick Verovic
The aim of this paper is to provide two examples in Hilbert geometry which show that volume growth entropy is not always a limit on the one hand, and that it may vanish for a non-p…
Isoperimetric control of the spectrum of a compact hypersurface
Bruno Colbois, Ahmad El Soufi, Alexandre Girouard
Upper bounds for the eigenvalues of the Laplace-Beltrami operator on a hypersurface bounding a domain in some ambient Riemannian manifold are given in terms of the isoperimetric ra…
Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds
Bruno Colbois, Emily B. Dryden, Ahmad El Soufi
We give upper bounds for the eigenvalues of the La-place-Beltrami operator of a compact -dimensional submanifold of . Besides the dimension and the volume of the s…
Hilbert geometry for convex polygonal domains
Bruno Colbois, Constantin Vernicos, Patrick Verovic
We prove in this paper that the Hilbert geometry associated with an open convex polygonal set is Lipschitz equivalent to Euclidean plane.