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

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

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

Sur la L2-cohomologie des varietes a courbure negative

New version. We improve our main result, which is now optimalWe give a topological interpretation of the space of L2-harmonic forms on finite-volume manifolds with sufficiently pinched negative curvature. We give examples showing that this interpretation fails if the curvature is not sufficiently pinched and that our result is sharp with respect to the pinching constants. The method consists first in comparing L2-cohomology with weighted L2-cohomology thanks to previuos works done by T. Ohsawa, and then in identifying these weighted spaces

Relation between Exponential Stability and Input-to-State Stability of Time-Delay Systems

International audienceThe main contribution of this paper is to establish a link between the exponential stability of an unforced system and the Input-to-State Stability (ISS) via the Lyapunov- Krasovskii methodology. A new theorem is provided, which proves that an unforced system whose trivial solution is exponentially stable is input-to-state stable if submitted to a perturbation which can be of an arbitrary size