# Formes harmoniques L2 sur les varietes a courbure negative

Abstract : We study the spaces of $L^2$ harmonic forms, mainly on finite volume manifolds with pinched negative curvature. We want to give a topological interpretation of these spaces. We first show such an interpretation if the curvature is sufficiently pinched. We also construct examples which prove that our curvature hypothesis is necessary and sharp. We then consider manifolds which are besides Kaehler, and we show that without any assumption on the pinching, we can give a topological interpretation of the space of $L^2$ harmonic k-forms, for suitable k's. We finally study more generally the $L^p$-cohomology of our manifolds.
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https://tel.archives-ouvertes.fr/tel-00003778
Submitted on : Tuesday, November 18, 2003 - 2:10:53 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Wednesday, September 12, 2012 - 11:40:40 AM

### Identifiers

• HAL Id : tel-00003778, version 1

### Citation

Nader Yeganefar. Formes harmoniques L2 sur les varietes a courbure negative. Mathématiques [math]. Université de Nantes, 2003. Français. ⟨tel-00003778⟩

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