Une inégalité universelle pour la première valeur propre du laplacien
Une représentation gaussienne de l'indice d'un opérateur
Une suite exacte en -cohomologie
Une version microlocale de la condition de Verdier
Kashiwara et Schapira ont proposé une condition de régularité appelée ( sur un couple de sous-variétés d’une variété , où est une somme géométrique naturelle dans l’analyse microlocale. Nous démontrons que la )-régularité est équivalente à la -régularité de Verdier, répondant ainsi à une question de Kashiwara.
Unicité forte à partir d'une variété de dimension quelconque pour des inégalités différentielles elliptiques
Uniform controllability for the beam equation with vanishing structural damping
This paper is devoted to studying the effects of a vanishing structural damping on the controllability properties of the one dimensional linear beam equation. The vanishing term depends on a small parameter . We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls as goes to zero. It is shown that for any time sufficiently large but independent of and for each initial data in a suitable space there exists a uniformly bounded...
Uniqueness for the harmonic map flow from surface to general targets.
Uniqueness of conformal metrics with prescribed scalar and mean curvatures on compact manifolds with boundary.
Uniqueness of global positive solution branches of nonlinear elliptic problems.
Uniqueness of Harmonie Mappings and of Solutions of Elliptic Equations on Riemannnian Manifolds.
Uniqueness of motion by mean curvature perturbed by stochastic noise
Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains
Unitons and their moduli.
Universal bounds for eigenvalues of Schrödinger operators on Riemannian manifolds.
Universal prolongation of linear partial differential equations on filtered manifolds
The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.
Untere Schranken für den ersten Eigenwert des Laplace-Operators auf kompakten Riemannschen Flächen.
Upper bound for the first eigenvalue of algebraic submanifolds.
Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds
On geometrically finite hyperbolic manifolds , including those with non-maximal rank cusps, we give upper bounds on the number of resonances of the Laplacian in disks of size as . In particular, if the parabolic subgroups of satisfy a certain Diophantine condition, the bound is .