L2-cohomology of negatively curved Kaehler manifolds of finite volume

We compute the space of $L^2$ harmonic forms (outside the middle degrees) on negatively curved Kaehler manifolds of finite volume

Embeddability of some strongly pseudoconvex CR manifolds

We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kaehler manifolds with compact strongly pseudoconvex boundary. An embedding theorem for Sasakian manifolds is also derived.Comment: 12 pages, AMSLate

Lp-cohomology of negatively curved manifolds

We compute the $L^p$-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds

K\"ahler-Einstein fillings

We show that on an open bounded smooth strongly pseudoconvex subset of \CC^{n}, there exists a K\"ahler-Einstein metric with positive Einstein constant, such that the metric restricted to the Levi distribution of the boundary is conformal to the Levi form. To achieve this, we solve an associated complex Monge-Amp\`ere equation with Dirichlet boundary condition. We also prove uniqueness under some more assumptions on the open set.Comment: 27 page

Finite-time stability and stabilization of time-delay systems

International audienceFinite-time stability and stabilization of retarded-type functional differential equations are developed. First, a theoretical result on finite-time stability inspired by the theory of differential equations, using Lyapunov functionals, is given. As it may appear not easily usable in practice, we show how to obtain finite-time stabilization of linear systems with delays in the input by using an extension of Artstein's model reduction to nonlinear feedback. With this approach, we give an explicit finite-time controller for scalar linear systems and for the chain of integrators with delays in the input