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.
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 .
We discuss variational integrals which are defined on differential forms associated with a given first order elliptic complex. This general framework provides us with better understanding of the concepts of convexity, even in the classical setting
Dans cet article, nous nous intéresserons à certaines propriétés des variétés riemanniennes non compactes qui ne dépendant que de leur géométrie à l'infini; pour cela, nous utiliserons un procédé de discrétisation qui associe un graph (pondéré) à une variété.