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# Some New Results on $L^2$ Cohomology of Negatively Curved Riemannian Manifolds

The present paper is concerned with the study of the $L^2$ cohomology spaces of negatively curved manifolds. The first half presents a finiteness and vanishing result obtained under some curvature assumptions, while the second half identifies a class of metrics having non-trivial $L^2$ cohomology for degree equal to the half dimension of the space. For the second part we rely on the existence and regularity properties of the solution for the heat equation for forms.