On the differential form spectrum of hyperbolic manifolds

Carron, Gilles; Pedon, Emmanuel

Carron, Gilles ¹ ; Pedon, Emmanuel ²

¹ Laboratoire de Mathématiques Jean Leray (UMR 6629) Université de Nantes 2 rue de la Houssinière B.P. 92208 44322 Nantes Cedex 3, France
² Laboratoire de Mathématiques (UMR 6056) Université de Reims Moulin de la Housse B.P. 1039 51687 Reims Cedex 2, France

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 4, pp. 705-747.

Résumé

We give a lower bound for the bottom of the $L^{2}$ differential form spectrum on hyperbolic manifolds, generalizing thus a well-known result due to Sullivan and Corlette in the function case. Our method is based on the study of the resolvent associated with the Hodge-de Rham laplacian and leads to applications for the (co)homology and topology of certain classes of hyperbolic manifolds.

MR Zbl | 2 citations dans Numdam

Classification : 53C35, 22E40, 34L15, 57T15, 58J50

Affiliations des auteurs :

Carron, Gilles ¹ ; Pedon, Emmanuel ²

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Carron, Gilles; Pedon, Emmanuel. On the differential form spectrum of hyperbolic manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 4, pp. 705-747. http://archive.numdam.org/item/ASNSP_2004_5_3_4_705_0/

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