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.
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.
Keywords: $L^2$ harmonic form, hyperbolic manifold, critical exponent
Mot 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{\textquoteright}institut Fourier}, volume = {60}, number = {7}, year = {2010}, doi = {10.5802/aif.2608}, zbl = {1236.53040}, mrnumber = {2848671}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2608/} }
TY - JOUR AU - Carron, Gilles TI - Rigidity and $L^2$ cohomology of hyperbolic manifolds JO - Annales de l'Institut Fourier PY - 2010 SP - 2307 EP - 2331 VL - 60 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2608/ DO - 10.5802/aif.2608 LA - en ID - AIF_2010__60_7_2307_0 ER -
%0 Journal Article %A Carron, Gilles %T Rigidity and $L^2$ cohomology of hyperbolic manifolds %J Annales de l'Institut Fourier %D 2010 %P 2307-2331 %V 60 %N 7 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2608/ %R 10.5802/aif.2608 %G en %F 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://www.numdam.org/articles/10.5802/aif.2608/
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