Spectre d'une variété privée d'un ɛ-tube (Conditions de Dirichlet)
Spectrum and Holonomy of the Line Bundle over the Sphere.
Spectrum of 2-dimensional manifolds
Spectrum of a compact flat manifold.
Spectrum of the Laplace operator and periodic geodesics: thirty years after
What is called the “Semi-classical trace formula” is a formula expressing the smoothed density of states of the Laplace operator on a compact Riemannian manifold in terms of the periodic geodesics. Mathematical derivation of such formulas were provided in the seventies by several authors. The main goal of this paper is to state the formula and to give a self-contained proof independent of the difficult use of the global calculus of Fourier Integral Operators. This proof is close in the spirit of...
Spectrum of the laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions
We consider the laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one...
Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions
We consider the Laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one...
Spectrum of the Laplacian in narrow tubular neighbourhoods of hypersurfaces with combined Dirichlet and Neumann boundary conditions
We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the hypersurfaces tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the area of the Neumann...
Spectrum of the Poincaré Map for Periodic Reflecting Rays in Generic Domains.
Spektrale Starrheit gewisser Drehflächen.
Stable minimal cones in and with constant scalar curvature.
Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equations
Let (M,g) be a compact Riemannian manifold without boundary, with dim M ≥ 3, and f: ℝ → ℝ a continuous function which is sublinear at infinity. By various variational approaches, existence of multiple solutions of the eigenvalue problem , σ ∈ M, ω ∈ H₁²(M), is established for certain eigenvalues λ > 0, depending on further properties of f and on explicit forms of the function K̃. Here, stands for the Laplace-Beltrami operator on (M,g), and α, K̃ are smooth positive functions. These multiplicity...
Sur la mulitplicité de la première valeur propre non nulle du Laplacien.
Sur la multiplicité de la première valeur propre d'une surface de Riemann à courbure constante.
Sur la multiplicité des valeurs propres du laplacien
Sur la multiplicité des valeurs propres d’une variété compacte
Dans ce survol, on rappelle les résultats connus sur la multiplicité des valeurs propres du laplacien sur une variété compacte, et on présente des résultats nouveaux concernant les valeurs propres multiples du laplacien de Hodge-de Rham.
Sur la première valeur propre des tores
Sur la théorie spectrale de quelques variétés non compactes
Sur la théorie spectrale des problèmes aux limites pseudo-différentiels elliptiques
Sur le noyau de la chaleur associé aux puissances tensorielles d'un fibré en droites complexes. Estimations asymptotiques et théorèmes d'annulation