Conformal Dirichlet-Neumann maps and Poincaré-Einstein manifolds.
Counterexamples to the Strichartz inequalities for the wave equation in general domains with boundary
In this paper we consider a smooth and bounded domain of dimension with boundary and we construct sequences of solutions to the wave equation with Dirichlet boundary condition which contradict the Strichartz estimates of the free space, providing losses of derivatives at least for a subset of the usual range of indices. This is due to microlocal phenomena such as caustics generated in arbitrarily small time near the boundary. Moreover, the result holds for microlocally strictly convex domains...
Critical points at infinity in the variational calculus
Déterminant relatif et la fonction Xi
Déterminants et intégrales de Fresnel
On présente ici une approche directe et géométrique pour le calcul des déterminants d’opérateurs de type Schrödinger sur un graphe fini. Du calcul de l’intégrale de Fresnel associée, on déduit le déterminant. Le calcul des intégrales de Fresnel est grandement facilité par l’utilisation simultanée du théorème de Fubini et d’une version linéaire du calcul symbolique des opérateurs intégraux de Fourier. On obtient de façon directe une formule générale exprimant le déterminant en terme des conditions...
Elliptic boundary problems on spaces with conic points
Functional determinants and geometry .
Functional determinants and geometry (Erratum).
Generalized Dirac Operators on Nonsmooth Manifolds and Maxwell's Equations.
Geometric P.D.E.'s with isolated singularities.
Harmonic maps between unbounded convex polyhedra in hyperbolic spaces.
Hypersurfaces of constant curvature in hyperbolic space II
This is the second of a series of papers in which we investigate the problem of finding, in hyperbolic space, complete hypersurfaces of constant curvature with a prescribed asymptotic boundary at infinity for a general class of curvature functions. In this paper we focus on graphs over a domain with nonnegative mean curvature.
Index theory and elliptic boundary value problems. Remarks and open problems
Interface and mixed boundary value problems on -dimensional polyhedral domains.
K-theory of Boutet de Monvel's algebra
We consider the norm closure 𝔄 of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact manifold X with boundary ∂X. Assuming that all connected components of X have nonempty boundary, we show that K₁(𝔄) ≃ K₁(C(X)) ⊕ ker χ, where χ: K₀(C₀(T*Ẋ)) → ℤ is the topological index, T*Ẋ denoting the cotangent bundle of the interior. Also K₀(𝔄) is topologically determined. In case ∂X has torsion free K-theory, we get K₀(𝔄) ≃ K₀(C(X)) ⊕ K₁(C₀(T*Ẋ)).
Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups
Les singularités des fonctions spectrales sur une variété riemannienne infiniment aplatie
Levi's forms of higher codimensional submanifolds
Let , let be a hypersurface of , be a submanifold of . Denote by the Levi form of at . In a previous paper [3] two numbers , are defined; for they are the numbers of positive and negative eigenvalues for . For , , we show here that are still the numbers of positive and negative eigenvalues for when restricted to . Applications to the concentration in degree for microfunctions at the boundary are given.
Ljusternik-Schnirelmann theory on -manifolds
Maximal functions related to subelliptic operators invariant under an action of a nilpotent Lie group