In mathematics, Mostow's rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a complete...

representation of G giving rise to ρ by restriction. Mostow rigidity theorem Local rigidity Margulis 1991, p. 2 Theorem 2. "Discrete subgroup", Encyclopedia of Mathematics...

any manifold of genus at least two has a hyperbolic structure. Mostow's rigidity theorem does not apply in this case. In fact, there are many hyperbolic...

completely determined by its values on any set of basis vectors of X. Mostow's rigidity theorem, which states that the geometric structure of negatively curved...

of M has a complete hyperbolic structure of finite volume. The Mostow rigidity theorem implies that if a manifold of dimension at least 3 has a hyperbolic...

Mostow may refer to: George Mostow (1923–2017), American mathematician Mostow rigidity theorem Jonathan Mostow (born 1961), American movie and television...

to 1992. The rigidity phenomenon for lattices in Lie groups he discovered and explored is known as Mostow rigidity. His work on rigidity played an essential...

boundary of the manifold. The ending lamination theorem is a generalization of the Mostow rigidity theorem to hyperbolic manifolds of infinite volume. When...

completely understood. Those of finite volume can be understood via the Mostow rigidity theorem. For hyperbolic local geometry, many of the possible three-dimensional...

(differential geometry) Mostow rigidity theorem (differential geometry) Myers theorem (differential geometry) Myers-Steenrod theorem (differential geometry)...

conjecture Cartan–Hadamard theorem Collapsing manifold Lévy–Gromov inequality Taubes's Gromov invariant Mostow rigidity theorem Ramsey–Dvoretzky–Milman phenomenon...

Thurston observes that this uniqueness is a consequence of the Mostow rigidity theorem. To see this, let G be represented by a circle packing. Then the...

Kleinian model. Dini's surface Hyperbolic 3-manifold Ideal polyhedron Mostow rigidity theorem Murakami–Yano formula Pseudosphere Grigor'yan, Alexander; Noguchi...

many (up to conjugation) lattices with covolume bounded by v. The Mostow rigidity theorem states that for lattices in simple Lie groups not locally isomorphic...

hyperbolic geometry of a 3-manifold to its topology also comes from the Mostow rigidity theorem, which states that the hyperbolic structure of a hyperbolic 3-manifold...

trivial. It is different from Mostow rigidity and weaker (but holds more frequently) than superrigidity. The first such theorem was proven by Atle Selberg...

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...

of M has a complete hyperbolic structure of finite volume. The Mostow rigidity theorem implies that if a manifold of dimension at least 3 has a hyperbolic...

boundaries. This result is the first step in the proof of the Mostow rigidity theorem. Furthermore, this result has found utility in analyzing user interaction...

polynomial growth theorem; Stallings' ends theorem; Mostow rigidity theorem. Quasi-isometric rigidity theorems, in which one classifies algebraically all...

between them can be homotoped to homeomorphisms. For instance, the Mostow rigidity theorem states that a homotopy equivalence between closed hyperbolic manifolds...

positively-curved manifolds have finite fundamental group (see Myers' theorem). Mostow's rigidity theorem: for compact hyperbolic manifolds of dimension at least 3...

and simpler proof of the Mostow rigidity theorem. 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 Mostow rigidity theorem fame and Calvin Hill, NFL Rookie of the Year and...

are relatively well understood. Deep results of Borel, Harish-Chandra, Mostow, Tamagawa, M. S. Raghunathan, Margulis, Zimmer obtained from the 1950s through...

{R} )} , with trivial center and no compact factors, then by the Mostow rigidity theorem, the abstract commensurator of any irreducible lattice Γ ≤ G {\displaystyle...

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...

finite volume hyperbolic n {\displaystyle n} -manifold is unique by Mostow rigidity and so geometric invariants are in fact topological invariants. One...

The peripheral subgroup can also work as a complete invariant. By Mostow–Prasad rigidity, the hyperbolic structure on the complement of a hyperbolic link...

{\displaystyle vol(X)=\sum _{j=1}^{n}D_{2}(z)} by gluing them. The Mostow rigidity theorem guarantees only single value of the volume with Im   z j > 0 {\displaystyle...