Sur la L 2 -cohomologie des variétés à courbure négative

Abstract

We give a topological interpretation of the space of $L^2$-harmonic forms of 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 $L^2$-cohomology with weighted $L^2$-cohomology thanks to previous works done by T. Ohsawa, and then in identifying these weighted spaces.