Mostow's rigidity theorem does not apply in this case.
2.
Thurston observes that this uniqueness is a consequence of the Mostow rigidity theorem.
3.
The Mostow rigidity theorem may be stated as:
4.
This result is the first step in the proof of the Mostow rigidity theorem.
5.
This is another example of a rigidity theorem.
6.
The ending lamination theorem is a generalization of the Mostow rigidity theorem to hyperbolic manifolds of infinite volume.
7.
The geometry of Hadamard spaces resembles that of Hilbert spaces, making it a natural setting for the study of rigidity theorems.
8.
When the manifold is compact or of finite volume, the Mostow rigidity theorem states that the fundamental group determines the manifold.
9.
For instance, the Mostow rigidity theorem states that a homotopy equivalence between closed hyperbolic manifolds is homotopic to an isometry in particular, to a homeomorphism.
10.
He was aware of the Mostow rigidity theorem for locally symmetric spaces, which he used to prove the uniqueness of complex structure of quotients of complex balls.
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