Geometriae Dedicata

, Volume 117, Issue 1, pp 111–124

Maximal Volume Representations are Fuchsian

Article

DOI: 10.1007/s10711-005-9033-0

Cite this article as:
Francaviglia, S. & Klaff, B. Geom Dedicata (2006) 117: 111. doi:10.1007/s10711-005-9033-0

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’

Keywords

hyperbolic geometryrigiditynatural maps

Mathematics Subject Classification (2000)

51M10

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Universitat Autònoma de BarcelonaBarcelonaSpain
  2. 2.University of TexasTexasU.S.A.