When 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 harmonic forms vanish. In this paper, we show rigidity results in the borderline case of these vanishing results.
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 . 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.
Classification: 58J50, 22E40
Keywords: harmonic form, hyperbolic manifold, critical exponent
@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},
publisher = {Association des Annales de l'institut Fourier},
volume = {60},
number = {7},
year = {2010},
pages = {2307-2331},
doi = {10.5802/aif.2608},
mrnumber = {2848671},
zbl = {1236.53040},
language = {en},
url = {http://www.numdam.org/item/AIF_2010__60_7_2307_0}
}
Carron, Gilles. Rigidity and $L^2$ cohomology of hyperbolic manifolds. Annales de l'Institut Fourier, Volume 60 (2010) no. 7, pp. 2307-2331. doi : 10.5802/aif.2608. http://www.numdam.org/item/AIF_2010__60_7_2307_0/
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