TY - JOUR
T1 - Maximal volume representations are fuchsian
AU - Francaviglia, Stefano
AU - Klaff, Ben
PY - 2006/2/1
Y1 - 2006/2/1
N2 - 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.
AB - 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.
KW - Hyperbolic geometry
KW - Natural maps
KW - Rigidity
UR - https://www.scopus.com/pages/publications/33646568448
U2 - 10.1007/s10711-005-9033-0
DO - 10.1007/s10711-005-9033-0
M3 - Article
SN - 0046-5755
VL - 117
SP - 111
EP - 124
JO - Geometriae Dedicata
JF - Geometriae Dedicata
IS - 1
ER -