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Hyperbolic manifolds, amalgamated products and critical exponents

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Title: Hyperbolic manifolds, amalgamated products and critical exponents
Alternate Title: Varie´te´s hyperboliques, produits amalgame´s et exposants critiques
Authors: Besson, Gérard1 G.Besson@fourier.ujf-grenoble.fr, Courtois, Gilles2 courtois@math.polytechnique.fr, Gallot, Sylvestre1 Sylvestre.Gallot@fourier.ujf-grenoble.fr
Source: Comptes Rendus. Mathématique. Feb2003, Vol. 336 Issue 3, p257. 5p.
Subjects: Hyperbolic spaces, Curvature
Abstract (English): We give a new proof of a result due to Y. Shalom: if the fundamental group of a compact real hyperbolic manifold of dimn is a free product of its subgroups A and B over the amalgamated subgroup C, then the critical exponent of C is not smaller than n−2. The proof, which is geometric, allows one to treat the equality case and an extension to variable curvature. To cite this article: G. Besson et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003). [Copyright &y& Elsevier]
Abstract (French): Nous donnons une preuve nouvelle d'un re´sultat duˆ a` Y. Shalom ; pre´cise´ment, nous montrons que, si le groupe fondamental d'une varie´te´ hyperbolique re´elle compacte de dimension n est le produit libre de ses sous-groupes A et B amalgame´ sur C, alors l'exposant critique de C est plus grand que n−2. La preuve, ge´ome´trique, permet de traiter le cas d'e´galite´ ainsi qu'une extension au cas de courbure variable. Pour citer cet article : G. Besson et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003). [Copyright 2003 Elsevier]
Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Hyperbolic manifolds, amalgamated products and critical exponents
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  Data: Varie´te´s hyperboliques, produits amalgame´s et exposants critiques
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  Data: <searchLink fieldCode="JN" term="%22Comptes+Rendus%2E+Mathématique%22">Comptes Rendus. Mathématique</searchLink>. Feb2003, Vol. 336 Issue 3, p257. 5p.
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  Data: We give a new proof of a result due to Y. Shalom: if the fundamental group of a compact real hyperbolic manifold of <f>dimn</f> is a free product of its subgroups <f>A</f> and <f>B</f> over the amalgamated subgroup <f>C</f>, then the critical exponent of <f>C</f> is not smaller than <f>n−2</f>. The proof, which is geometric, allows one to treat the equality case and an extension to variable curvature. To cite this article: G. Besson et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003). [Copyright &y& Elsevier]
– Name: Abstract
  Label: Abstract (French)
  Group: Ab
  Data: Nous donnons une preuve nouvelle d'un re´sultat duˆ a` Y. Shalom ; pre´cise´ment, nous montrons que, si le groupe fondamental d'une varie´te´ hyperbolique re´elle compacte de dimension <f>n</f> est le produit libre de ses sous-groupes <f>A</f> et <f>B</f> amalgame´ sur <f>C</f>, alors l'exposant critique de <f>C</f> est plus grand que <f>n−2</f>. La preuve, ge´ome´trique, permet de traiter le cas d'e´galite´ ainsi qu'une extension au cas de courbure variable. Pour citer cet article : G. Besson et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003). [Copyright 2003 Elsevier]
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  Data: <i>Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              Text: Feb2003
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