In mathematics, Mostow's rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a complete, finite-volume hyperbolic manifold of dimension greater than two is determined by the fundamental group and hence unique. The theorem was proven for closed manifolds by Mostow (1968) and extended to finite volume manifolds by Marden (1974) in 3 dimensions, and by Prasad (1973) in all dimensions at least 3. Gromov (1981) gave an alternate proof using the Gromov norm. Besson, Courtois & Gallot (1996) gave the simplest available proof.
While the theorem shows that the deformation space of (complete) hyperbolic structures on a finite volume hyperbolic -manifold (for ) is a point, for a hyperbolic surface of genus there is a moduli space of dimension that parameterizes all metrics of constant curvature (up to diffeomorphism), a fact essential for Teichmüller theory. There is also a rich theory of deformation spaces of hyperbolic structures on infinite volume manifolds in three dimensions.
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In mathematics, Mostow'srigiditytheorem, or strong rigiditytheorem, or Mostow–Prasad rigiditytheorem, essentially states that the geometry of a complete...
to 1992. The rigidity phenomenon for lattices in Lie groups he discovered and explored is known as Mostowrigidity. His work on rigidity played an essential...
Mostow may refer to: George Mostow (1923–2017), American mathematician Mostowrigiditytheorem Jonathan Mostow (born 1961), American movie and television...
boundary of the manifold. The ending lamination theorem is a generalization of the Mostowrigiditytheorem to hyperbolic manifolds of infinite volume. When...
any manifold of genus at least two has a hyperbolic structure. Mostow'srigiditytheorem does not apply in this case. In fact, there are many hyperbolic...
completely understood. Those of finite volume can be understood via the Mostowrigiditytheorem. For hyperbolic local geometry, many of the possible three-dimensional...
representation of G giving rise to ρ by restriction. Mostowrigiditytheorem Local rigidity Margulis 1991, p. 2 Theorem 2. "Discrete subgroup", Encyclopedia of Mathematics...
of M has a complete hyperbolic structure of finite volume. The Mostowrigiditytheorem implies that if a manifold of dimension at least 3 has a hyperbolic...
between them can be homotoped to homeomorphisms. For instance, the Mostowrigiditytheorem states that a homotopy equivalence between closed hyperbolic manifolds...
Thurston observes that this uniqueness is a consequence of the Mostowrigiditytheorem. To see this, let G be represented by a circle packing. Then the...
polynomial growth theorem; Stallings' ends theorem; Mostowrigiditytheorem. Quasi-isometric rigiditytheorems, in which one classifies algebraically all...
and simpler proof of the Mostowrigiditytheorem. The result of Besson, Courtois, and Gallo is called minimal entropy rigidity. In 1998 he was an invited...
actor George Takei (Sulu of Star Trek fame) to G. D. Mostow the mathematician of Mostowrigiditytheorem fame and Calvin Hill, NFL Rookie of the Year and...
trivial. It is different from Mostowrigidity and weaker (but holds more frequently) than superrigidity. The first such theorem was proven by Atle Selberg...
are relatively well understood. Deep results of Borel, Harish-Chandra, Mostow, Tamagawa, M. S. Raghunathan, Margulis, Zimmer obtained from the 1950s through...
curved symmetric spaces by Mostow, for his work on the rigidity of discrete groups. The basic result is the Morse–Mostow lemma on the stability of geodesics...
result can be recovered from the combination of Mostowrigidity with Thurston's geometrization theorem. Note that some families of examples are contained...
{\displaystyle vol(X)=\sum _{j=1}^{n}D_{2}(z)} by gluing them. The Mostowrigiditytheorem guarantees only single value of the volume with Im z j > 0 {\displaystyle...
finite volume hyperbolic n {\displaystyle n} -manifold is unique by Mostowrigidity and so geometric invariants are in fact topological invariants. One...
cohomology, they proved the rigidity of higher-dimensional cases. Their work was an influence on the later work of George Mostow and Grigori Margulis, who...
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