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Quasi-conformal geometry and hyperbolic geometry. (English) Zbl 1002.30012

Burger, Marc (ed.) et al., Rigidity in dynamics and geometry. Contributions from the programme Ergodic theory, geometric rigidity and number theory, Isaac Newton Institute for the Mathematical Sciences, Cambridge, UK, January 5-July 7, 2000. Berlin: Springer. 1-17 (2002).
The authors study the connection of quasiconformal and hyperbolic geometry. The present paper gives a survey of these fields. In particular, the existence of Poincaré inequalities with respect to applications to Gromov hyperbolic spaces is discussed and the proofs of the rigidity of quasiisometries in the case of quaternionic and Cayley hyperbolic spaces [See P. Pansu, Ann. Math., II. Ser. 129, No.1, 1-60 (1989; Zbl 0678.53042)] are described.
For the entire collection see [Zbl 0987.00036].

MSC:

30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations

Citations:

Zbl 0678.53042
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