Rigidity and L 2 cohomology of hyperbolic manifolds
[Rigidité et cohomologie L 2 des variétés hyperboliques]
Carron, Gilles1
1 Université de Nantes Laboratoire de mathématiques Jean Leray 2, rue de la Houssinière BP 92208 44322 Nantes cedex 03 (France)
Annales de l'Institut Fourier, Tome 60 (2010) no. 7, pp. 2307-2331.

La petitesse de l’exposant critique du groupe fondamental d’une variété hyperbolique implique des résultats d’annulation pour certains espaces de cohomologie et de formes harmoniques L 2 . Nous obtenons ici des résultats de rigidité reliés à ces théorèmes d’annulations. Ceci est une généralisation de résultats déjà connus dans le cas convexe co-compact.

When X=Γ∖ℍ n is a real hyperbolic manifold, it is already known that if the critical exponent is small enough then some cohomology spaces and some spaces of L 2 harmonic forms vanish. In this paper, we show rigidity results in the borderline case of these vanishing results.

DOI : 10.5802/aif.2608
Classification : 58J50, 22E40
Keywords: $L^2$ harmonic form, hyperbolic manifold, critical exponent
Mot clés : formes harmoniques $L^2$, variété hyperbolique, exposant critique
Carron, Gilles 1

1 Université de Nantes Laboratoire de mathématiques Jean Leray 2, rue de la Houssinière BP 92208 44322 Nantes cedex 03 (France) 
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Carron, Gilles. Rigidity and $L^2$ cohomology  of hyperbolic manifolds. Annales de l'Institut Fourier, Tome 60 (2010) no. 7, pp. 2307-2331. doi : 10.5802/aif.2608. http://www.numdam.org/articles/10.5802/aif.2608/

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