WebIt is a careful and detailed introduction to the higher-dimensional theory of quasiconformal mappings from the geometric viewpoint, based primarily on the technique of the conformal modulus of a curve family. Notably, the final chapter describes the application of quasiconformal mapping theory to Mostow's celebrated rigidity theorem in its ... WebIn mathematics, Mostow's rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a complete, …

Rigidity (mathematics) - Wikipedia

WebTheorem (Mostow rigidity) 7.1. Let and be oriented closed connected hyperbolic manifolds of the same dimension . If is a homotopy equivalence, then there is an isometry … WebOn the other hand, Mostow’s Rigidity Theorem is also true for the nite volume case. Our aim is to give three di erent proofs of Mostow’s Rigidity Theorem: a proof given by … high grade cgin

Hyperbolic 3-manifold - Wikipedia

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)). 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 … 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 … See more The theorem can be given in a geometric formulation (pertaining to finite-volume, complete manifolds), and in an algebraic formulation (pertaining to lattices in Lie groups). Geometric form See more It follows from the Mostow rigidity theorem that the group of isometries of a finite-volume hyperbolic n-manifold M (for n>2) is finite and … See more • Superrigidity, a stronger result for higher-rank spaces • Local rigidity, a result about deformations that are not necessarily lattices. See more high grade chondrosis