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 : https://doi.org/10.5802/aif.2608
Classification : 58J50,  22E40
Mots clés : formes harmoniques L 2 , variété hyperbolique, exposant critique
@article{AIF_2010__60_7_2307_0,
     author = {Carron, Gilles},
     title = {Rigidity and $L^2$ cohomology  of hyperbolic manifolds},
     journal = {Annales de l'Institut Fourier},
     pages = {2307--2331},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {60},
     number = {7},
     year = {2010},
     doi = {10.5802/aif.2608},
     mrnumber = {2848671},
     zbl = {1236.53040},
     language = {en},
     url = {archive.numdam.org/item/AIF_2010__60_7_2307_0/}
}
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://archive.numdam.org/item/AIF_2010__60_7_2307_0/

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