Rigidity and L 2 cohomology of hyperbolic manifolds
[Rigidité et cohomologie L 2 des variétés hyperboliques]
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 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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