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Artigo Acesso aberto Revisado por pares
BIBTEX RIS

Capacity differentials on open Riemann surfaces

1962; Mathematical Sciences Publishers; Volume: 12; Issue: 2 Linguagem: Inglês

10.2140/pjm.1962.12.769

ISSN

1945-5844

Autores

George Weill,

Tópico(s)

Meromorphic and Entire Functions

Resumo

WEILL ω e Γ Msey) Π Γ Moδ) , ( ω = 0, and ( ωf = 0.It follows that (ω, df*) = 0. J Y$ J δConversely, if (ω, df*) = 0, then ΣiΛ.l ω + \ ωf = 0 . Jγ$ J δSelect / = 1 on one of the y i9 say 7» 0 , / = 0 an δ and all other y im It follows that \ ω = 0.This is true for any contour j iQ .Hence ωeΓ h{sey) .Now take}*= 0 on 7; then [ ωe/\.Then (ω, d/) = ( aι/= ^/γ .(ω + ί ω/ = I /γί ω.If ωeΓ Λ(seV) , then ί ω = 0, and (ω, df*) = Jϊj Jδ Jγ,£ Jγ0. Conversely if (ω, d/*) = 0, then Σf y .\ ω + \ ωf = 0. Take / = 1 Jγ$ J δ on 7 e Γ Λ .Then (ω, d/*) =\ ωf=\ ωf.If Jβ JΎ

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