Quasiisometry from different points of view

Dedicated to Professor Vladimir Ya. Gutlyanskii on the occasion of his 70th birthday. We provide various characterizations of quasiisometric homeomorphisms in [R.sup.n] raised by the geometric, metric, analytic, and modular approaches. Keywords. Quasiisometry, quasiconformality, bi-Lipschitz mappings, p-module of k-dimensional surface families, module of ring domains.
1. Introduction Quasiisometric (or bi-Lipschitz) homeomorphisms form a very important subclass of quasiconformal mappings and have deep applications in mathematics and mechanics. The main characterization of quasiisometry relies on a [...]