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- Mostow_rigidity_theorem abstract "In mathematics, Mostow's rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a 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 dimensions at least 3. Gromov (1981) gave an alternate proof using the Gromov norm.Weil (1960, 1962) proved a closely related theorem, that implies in particular that cocompact discrete groups of isometries of hyperbolic space of dimension at least 3 have no non-trivial deformations. While the theorem shows that the deformation space of (complete) hyperbolic structures on a finite volume hyperbolic n-manifold (for n > 2) is a point, for a hyperbolic surface of genus g > 1 there is a moduli space of dimension 6g − 6 that parameterizes all metrics of constant curvature (up to diffeomorphism), a fact essential for Teichmüller theory. In dimension three, there is a "non-rigidity" theorem due to Thurston called the hyperbolic Dehn surgery theorem; it allows one to deform hyperbolic structures on a finite volume manifold as long as changing homeomorphism type is allowed. In addition, there is a rich theory of deformation spaces of hyperbolic structures on infinite volume manifolds.".
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- Mostow_rigidity_theorem wikiPageExternalLink item?id=PMIHES_1968__34__53_0.
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- Mostow_rigidity_theorem wikiPageID "2782164".
- Mostow_rigidity_theorem wikiPageRevisionID "543131028".
- Mostow_rigidity_theorem hasPhotoCollection Mostow_rigidity_theorem.
- Mostow_rigidity_theorem subject Category:Differential_geometry.
- Mostow_rigidity_theorem subject Category:Hyperbolic_geometry.
- Mostow_rigidity_theorem subject Category:Theorems_in_geometry.
- Mostow_rigidity_theorem type Abstraction100002137.
- Mostow_rigidity_theorem type Communication100033020.
- Mostow_rigidity_theorem type Message106598915.
- Mostow_rigidity_theorem type Proposition106750804.
- Mostow_rigidity_theorem type Statement106722453.
- Mostow_rigidity_theorem type Theorem106752293.
- Mostow_rigidity_theorem type TheoremsInGeometry.
- Mostow_rigidity_theorem comment "In mathematics, Mostow's rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a 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 dimensions at least 3.".
- Mostow_rigidity_theorem label "Mostow rigidity theorem".
- Mostow_rigidity_theorem label "Mostow-Starrheit".
- Mostow_rigidity_theorem label "Teorema di rigidità di Mostow".
- Mostow_rigidity_theorem sameAs Mostow-Starrheit.
- Mostow_rigidity_theorem sameAs Teorema_di_rigidità_di_Mostow.
- Mostow_rigidity_theorem sameAs m.082bvy.
- Mostow_rigidity_theorem sameAs Q3984063.
- Mostow_rigidity_theorem sameAs Q3984063.
- Mostow_rigidity_theorem sameAs Mostow_rigidity_theorem.
- Mostow_rigidity_theorem wasDerivedFrom Mostow_rigidity_theorem?oldid=543131028.
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