Webof Mostow rigidity theorem. For our purpose we only need to recall how to prove that Vn kMk ≥ vol(M,hyp). Because M is hyperbolic it is provided with a straight operator. First define the notion of straight simplex of Mfby induction as follows: the straight k … WebIn mathematics, Mostow's rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a complete, …

Mostow rigidity theorem - Wikipedia

WebThe ending lamination theorem is a generalization of the Mostow rigidity theorem to hyperbolic manifolds of infinite volume. When the manifold is compact or of finite volume, the Mostow rigidity theorem states that the fundamental group determines the manifold. WebIt follows from Theorem 5.5 of that int M admits two complete hyperbolic structures of finite volume, one is G 1-invariant and the other is G 2-invariant. Mostow’s rigidity theorem implies that complete hyperbolic structures of finite volume on int M are unique up to isometry representing the identity map on Out (π 1 (M)). monaincha bog

Mostow rigidity theorem - en-academic.com

Some examples include: 1. Harmonic functions on the unit disk are rigid in the sense that they are uniquely determined by their boundary values. 2. Holomorphic functions are determined by the set of all derivatives at a single point. A smooth function from the real line to the complex plane is not, in general, determined by all its derivatives at a single point, but it is if we require additionally that it be pos… WebHere is a limited form of Mostow Rigidity: Theorem 1.1 (Mostow) Suppose that M1 and M2 are both compact hy-perbolic 3-manifolds. If there is a BL map f : M1 → M2 then … WebAs a consequence of Theorem 1, we also reprove Thurston’s strict version of Gromov’s degree inequality for hyperbolic manifolds. Note that this strict version generalizes … monai label pathology