2006
DOI: 10.1007/s10711-005-9033-0
|View full text |Cite
|
Sign up to set email alerts
|

Maximal Volume Representations are Fuchsian

Abstract: We prove a volume-rigidity theorem for fuchsian representations of fundamental groups of hyperbolic k-manifolds into Isom(H n ). Namely, we show that if M is a complete hyperbolic k-manifold with finite volume, then the volume of any representation of π 1 (M ) into Isom(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".

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

1
56
0
1

Year Published

2009
2009
2021
2021

Publication Types

Select...
7
1

Relationship

1
7

Authors

Journals

citations
Cited by 35 publications
(58 citation statements)
references
References 11 publications
1
56
0
1
Order By: Relevance
“…Then, F is a global isometry of H n . For a detailed proof about this, we refer to [13]. Therefore, ρ is a totally geodesic representation.…”
Section: So(2 1)mentioning
confidence: 98%
“…Then, F is a global isometry of H n . For a detailed proof about this, we refer to [13]. Therefore, ρ is a totally geodesic representation.…”
Section: So(2 1)mentioning
confidence: 98%
“…The following theorem (whose proof will be sketched in Section 6 and completely described in [14]) is an example of applications of Theorems 1.2 and 1.3. Measurable Cannon-Thurston maps.…”
Section: Theorem 13 -In the Hypotheses Of Theorem 12 There Existsmentioning
confidence: 99%
“…-The weak convergence of b s x to b x is enough to prove stronger convergences. For example, it can be shown that the derivatives of F εi converges the ones of F , whence one gets that the convergence of the ε-natural maps is locally uniform (see [14] for details).…”
Section: Annales De L'institut Fouriermentioning
confidence: 99%
“…Moreover, ρ is parabolic on one boundary component of M. Since is discrete, ρ(π 1 (M)) = < is a finite-index subgroup. By [Francaviglia and Klaff 2006]…”
Section: Whitehead Link Complementmentioning
confidence: 99%