On the differential form spectrum of hyperbolic manifolds

Gilles Carron; Emmanuel Pedon

Displaying similar documents to “On the differential form spectrum 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 spectral theory and dynamics of asymptotically hyperbolic manifolds

Julie Rowlett (2010)

Annales de l’institut Fourier

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We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the physical description of their quantum and classical mechanics. We conclude with a discussion of recent results, ideas, and conjectures.

Rigidity and $L^{2}$ cohomology of hyperbolic manifolds

Gilles Carron (2010)

Annales de l’institut Fourier

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When $X = Γ ∖ ℍ^{n}$ is a real hyperbolic manifold, it is already known that if the critical exponent is small enough then some cohomology spaces and some spaces of $L^{2}$ harmonic forms vanish. In this paper, we show rigidity results in the borderline case of these vanishing results.