摘要
Any covering Y→X of a hyperbolic Riemann surface X determines an inclusion of Teichmuller spaces T(X)→T(Y). This map is shown to be an isometry for the Teichmuller metric iff the covering is amenable, and contracting iff for any [μ]εT(X), where is the Poincare series operator. Furthermore the inclusion is not a uniform contraction on T(X).
Any covering Y→X of a hyperbolic Riemann surface X determines an inclusion of Teichmuller spaces T(X)→T(Y). This map is shown to be an isometry for the Teichmuller metric iff the covering is amenable, and contracting iff for any [μ]εT(X), where is the Poincare series operator. Furthermore the inclusion is not a uniform contraction on T(X).
