Displaying similar documents to “Rigidity of symmetric spaces”

On rank one symmetric space

Inkang Kim (2004-2005)

Séminaire de théorie spectrale et géométrie

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In this paper we survey some recent results on rank one symmetric space.

Tameness on the boundary and Ahlfors' measure conjecture

Jeffrey Brock, Kenneth Bromberg, Richard Evans, Juan Souto (2003)

Publications Mathématiques de l'IHÉS

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Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or , if one of the following conditions holds: 1. N has non-empty conformal boundary, 2. N is not homotopy equivalent to a compression body, or 3. N is a strong limit of geometrically finite manifolds. The first case proves Ahlfors’ measure conjecture for kleinian groups in the closure of the geometrically...

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 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.