On the differential form spectrum of hyperbolic manifolds

Details On the differential form spectrum of hyperbolic manifolds On the differential form spectrum of hyperbolic manifolds

2003-03-27

arxiv.org/abs/math/0303348v3

Ann. Sc. Norm. Super. Pisa Cl. Sci. III (2004) 705--747

Mathematics

Differential Geometry

Scientific paper

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.

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