, Volume 117, Issue 1, pp 111-124
Date: 29 Mar 2006

Maximal Volume Representations are Fuchsian

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Abstract

We prove a volume-rigidity theorem for Fuchsian representations of fundamental groups of hyperbolic k-manifolds into Isom \(\mathbb{H}^n\) . Namely, we show that if M is a complete hyperbolic k-manifold with finite volume, then the volume of any representation of π1(M) into isom \(\mathbb{H}^n\) , 3 ≤ kn, is less than the volume of M, and the volume is maximal if and only if the representation is discrete, faithful and ‘k-Fuchsian’

Stefano Francaviglia: Supported by an INdAM and a Marie Curie Intra European fellowship
Ben Klaff: Supported by a CIRGET fellowship and by the Chaire de Recherche du Canada en algèbre, combinatoire et informatique mathématique de l’UQAM.