We give a lower bound for the bottom of the 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.
@article{ASNSP_2004_5_3_4_705_0, author = {Carron, Gilles and Pedon, Emmanuel}, title = {On the differential form spectrum of hyperbolic manifolds}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {705--747}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 3}, number = {4}, year = {2004}, mrnumber = {2124586}, zbl = {1170.53309}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2004_5_3_4_705_0/} }
TY - JOUR AU - Carron, Gilles AU - Pedon, Emmanuel TI - On the differential form spectrum of hyperbolic manifolds JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2004 SP - 705 EP - 747 VL - 3 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2004_5_3_4_705_0/ LA - en ID - ASNSP_2004_5_3_4_705_0 ER -
%0 Journal Article %A Carron, Gilles %A Pedon, Emmanuel %T On the differential form spectrum of hyperbolic manifolds %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2004 %P 705-747 %V 3 %N 4 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2004_5_3_4_705_0/ %G en %F ASNSP_2004_5_3_4_705_0
Carron, Gilles; Pedon, Emmanuel. On the differential form spectrum of hyperbolic manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 4, pp. 705-747. http://www.numdam.org/item/ASNSP_2004_5_3_4_705_0/
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