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Uniformity of holomorphic families of non-homeomorphic planar Riemann surfaces. (English) Zbl 1300.32026
Summary: We show the variation formula for the Schiffer span $$s(t)$$ for moving Riemann surfaces $$R(t)$$ with $$t\in B=\{t\in \mathbb {C}\mid |t|<\rho \}$$, and apply it to show the simultaneous uniformization of moving planar Riemann surfaces of class $$O_{\text{AD}}$$.

##### MSC:
 32Q30 Uniformization of complex manifolds 32E10 Stein spaces, Stein manifolds 32Q28 Stein manifolds
##### Keywords:
uniformization; Stein manifold; Schiffer span; Riemann surface
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