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Details van artikel 85 van 164 gevonden artikelen
| Titel: |
Metrics of equicontinuity for riemann surfaces |
| Auteur: |
Fox, William C. |
| Verschenen in: |
Complex variables and elliptic equations |
| Paginering: | Jaargang 8 (1987) nr. 1-2 pagina's 19-28 |
| Jaar: |
1987-04 |
| Inhoud: |
We write δt(ε) 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(ε) goes to zero satisfies, for each ε the restriction [image omitted] 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[image omitted] 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 [image omitted] for 0<ε<1 That minimum coincides with the moduli at t of those B with |B(t)|= ε/2. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 85 van 164 gevonden artikelen
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