Mostow rigidity theorem
= Mostow rigidity theorem
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For complete finite-volume <hyperbolic space> manifolds of dimension at least three, an isomorphism of <fundamental groups> is induced, up to the usual basepoint-path choice, by a unique hyperbolic <isometry>. The finite-volume noncompact case includes the Prasad extension. Thus complete hyperbolic metrics on a fixed finite-volume three-manifold have no deformation moduli, unlike metrics on closed hyperbolic surfaces.