Teichmüller’s problem for Gromov hyperbolic domains

Let $${{\cal T}_K}\left( D \right)$$ be the class of K-quasiconformal automorphisms a domain ⊂ ℝn with identity boundary values. Teichmüller’s problem is to determine how far given point x ∈ can mapped under mapping $$f \in {{\cal . We estimate this distance between and f(x) from above by using two different metrics, ratio metric quasihyperbolic metric. study for Gromov hyperbolic domains in values at infinity. As applications, we obtain results on ψ-uniform inner uniform ℝn.