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Displaying similar documents to “On the spectral theory and dynamics of asymptotically hyperbolic manifolds”

On the differential form spectrum of hyperbolic manifolds

Gilles Carron, Emmanuel Pedon (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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.

Traces, lengths, axes and commensurability

Alan W. Reid (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.

On the distribution of resonances for some asymptotically hyperbolic manifolds

R. G. Froese, Peter D. Hislop (2000)

Journées équations aux dérivées partielles

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We establish a sharp upper bound for the resonance counting function for a class of asymptotically hyperbolic manifolds in arbitrary dimension, including convex, cocompact hyperbolic manifolds in two dimensions. The proof is based on the construction of a suitable paramatrix for the absolute S -matrix that is unitary for real values of the energy. This paramatrix is the S -matrix for a model laplacian corresponding to a separable metric near infinity. The proof of the upper bound on the...