On the differential form spectrum of hyperbolic manifolds
Carron, Gilles ; Pedon, Emmanuel
HAL, hal-00000264 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  cohomology,  Hodge-de Rham Laplacian,  hyperbolic manifolds,  locally symmetric spaces,  Hyperbolic spaces,  spectral theory,  53C35, 58J50; Secondary 22E40, 34L15, 57T15,  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG],  [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT],  [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] 
@article{hal-00000264,
     author = {Carron, Gilles and Pedon, Emmanuel},
     title = {On the differential form spectrum of hyperbolic manifolds},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00000264}
}

Carron, Gilles; Pedon, Emmanuel. On the differential form spectrum of hyperbolic manifolds. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00000264/