Représentations unitaires irréductibles des groupes simples complexes de rang deux
The purpose of this paper is to investigate Ricci-flatness of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups. We first show that if is a Ricci-flat left-invariant Lorentzian metric on a 2-step nilpotent Lie group , then the restriction of to the center of the Lie algebra of is degenerate. We then characterize the 2-step nilpotent Lie groups which can be endowed with a Ricci-flat left-invariant Lorentzian metric, and we deduce from this that a Heisenberg Lie group can be...
Let be a metric space, equipped with a Borel measure satisfying suitable compatibility conditions. An amalgam is a space which looks locally like but globally like . We consider the case where the measure of the ball with centre and radius behaves like a polynomial in , and consider the mapping properties between amalgams of kernel operators where the kernel behaves like when and like when . As an application, we describe Hardy–Littlewood–Sobolev type regularity theorems...
When is a real hyperbolic manifold, it is already known that if the critical exponent is small enough then some cohomology spaces and some spaces of harmonic forms vanish. In this paper, we show rigidity results in the borderline case of these vanishing results.