Quasiconformality and geometrical finiteness in Carnot--Carath\'eodory and negatively curved spaces

摘要: The paper sketches a recent progress and formulates several open problems in studying equivariant quasiconformal quasisymmetric homeomorphisms negatively curved spaces as well geometry topology of noncompact geometrically finite manifolds their boundaries at infinity having Carnot--Carath\'eodory structures. Especially, the most interesting are complex hyperbolic with Cauchy--Riemannian structure infinity, which occupy distinguished niche whose properties make them surprisingly different from real ones.