Maximal volume representations are fuchsian

Stefano Francaviglia, Ben Klaff

    Research output: Contribution to journalArticleResearchpeer-review

    16 Citations (Scopus)

    Abstract

    We prove a volume-rigidity theorem for Fuchsian representations of fundamental groups of hyperbolic k-manifolds into Isom(ℍn), 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(ℍn), 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'. © Springer 2006.
    Original languageEnglish
    Pages (from-to)111-124
    JournalGeometriae Dedicata
    Volume117
    Issue number1
    DOIs
    Publication statusPublished - 1 Feb 2006

    Keywords

    • Hyperbolic geometry
    • Natural maps
    • Rigidity

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