Rigidity and L 2 cohomology of hyperbolic manifolds

Gilles Carron[1]

  • [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 (2010)

  • Volume: 60, Issue: 7, page 2307-2331
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Carron, Gilles. "Rigidity and $L^2$ cohomology of hyperbolic manifolds." Annales de l’institut Fourier 60.7 (2010): 2307-2331. <http://eudml.org/doc/116335>.

@article{Carron2010,
abstract = {When $X=\Gamma \backslash \mathbb\{H\}^n$ 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.},
affiliation = {Université de Nantes Laboratoire de mathématiques Jean Leray 2, rue de la Houssinière BP 92208 44322 Nantes cedex 03 (France)},
author = {Carron, Gilles},
journal = {Annales de l’institut Fourier},
keywords = {$L^2$ harmonic form; hyperbolic manifold; critical exponent; harmonic form},
language = {eng},
number = {7},
pages = {2307-2331},
publisher = {Association des Annales de l’institut Fourier},
title = {Rigidity and $L^2$ cohomology of hyperbolic manifolds},
url = {http://eudml.org/doc/116335},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Carron, Gilles
TI - Rigidity and $L^2$ cohomology of hyperbolic manifolds
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 7
SP - 2307
EP - 2331
AB - When $X=\Gamma \backslash \mathbb{H}^n$ 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.
LA - eng
KW - $L^2$ harmonic form; hyperbolic manifold; critical exponent; harmonic form
UR - http://eudml.org/doc/116335
ER -

References

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