Integration of Monge-Ampère equations and surfaces with negative gaussian curvature
Interactions totalement non linéaires
estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III
Let be a symmetric space of the noncompact type, with Laplace–Beltrami operator , and let be the -spectrum of . For in such that , let be the operator on defined formally as . In this paper, we obtain operator norm estimates for for all , and show that these are optimal when is small and when is bounded below .
L’effet Hawking
Les singularités des fonctions spectrales sur une variété riemannienne infiniment aplatie
Local energy decay for several evolution equations on asymptotically euclidean manifolds
Let be a long range metric perturbation of the Euclidean Laplacian on , . We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger equations associated to . The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group where has a suitable development at zero (resp. infinity).
Local energy decay of solutions to the wave equation for nontrapping metrics
Moments and Huygens' principle for conformally invariant field equations in curved space-times
On contact equivalence of holomorphic Monge-Ampére equations.
On equivariant harmonic maps defined on a Lorentz manifold
In this paper, we prove by using the minimax principle that there exist infinitely many -equivariant harmonic maps from a specific Lorentz manifold to a compact Riemannian manifold.
On stabilization and control for the critical Klein-Gordon equation on a 3-D compact manifold
We study the internal stabilization and control of the critical nonlinear Klein-Gordon equation on 3-D compact manifolds. Under a geometric assumption slightly stronger than the classical geometric control condition, we prove exponential decay for some solutions bounded in the energy space but small in a lower norm. The proof combines profile decomposition and microlocal arguments. This profile decomposition, analogous to the one of Bahouri-Gérard [2] on , is performed by taking care of possible...
On the -singularities of regular holonomic distributions
The analytic and wave-front sets of a distribution which is a solution of a regular holonomic differential system are shown to coincide. More generally, we give comparison theorems for solutions of a regular holonomic system of microdifferential equations in various spaces of microfunctions, as a simple extension of a result of Kashiwara.
On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations [Book]
On the Initial-Boundary Value Problem for Harmonic Maps from the 2-Dimensional Minkowski Space.
On the wave equation in curved spacetime
Paramétrix de l'équation des ondes et intégrales sur l'espace des chemins
Propagation de singularités pour les opérateurs du type
Propagation des ondes dans les variétés à coins
Propagation des ondes dans les variétés à coins
Quantum vacuum polarization at the Black-Hole horizon