Metrics of equicontinuity for riemann surfaces
| Autor: | William C. Fox |
|---|---|
| Rok vydání: | 1987 |
| Předmět: | |
| Zdroj: | Complex Variables, Theory and Application: An International Journal. 8:19-28 |
| ISSN: | 1563-5066 0278-1077 |
| DOI: | 10.1080/17476938708814217 |
| Popis: | We write δt(e) for the modulus of continuity at t∈Δ of any holomorphic cover of a Riemann surface Z by the unit disk Δ That modulus is computed in terms of the absolute value metric for Δ and any metric σ a for Z's topology. THEOREM As t goes to the rim of Δ, the rate at which δt(e) goes to zero satisfies, for each e the restriction if and only if every family Hol(X, Z) is σ-equicontinuous {i.e. σ is a metric of equicontinuity for Z). In particular, that rate's dependence on σ satisfies the restriction when σ = dz, the Kobayashi distance (known to be a metric of equicontinuity when Z is hyperbolic). With Z ≡ Δ and σ as the absolute value metric, we also compute the minimum of the moduli at t of all biholomorphisms B of Δ to be for 0 |
| Databáze: | OpenAIRE |
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