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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
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