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 ≤ k ≤ n, is less than the volume of M, and the volume is maximal if and only if the representation is discrete, faithful and ‘k-Fuchsian’
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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.
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Francaviglia, S., Klaff, B. Maximal Volume Representations are Fuchsian. Geom Dedicata 117, 111–124 (2006). https://doi.org/10.1007/s10711-005-9033-0
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DOI: https://doi.org/10.1007/s10711-005-9033-0