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On Bloch seminorm of finite Blaschke products in the unit disk. (English) Zbl 1483.30100

Summary: We prove that, for any finite Blaschke product \(w = B(z)\) in the unit disk, the corresponding Riemann surface over the \(w\)-plane contains a one-sheeted disk of the radius 0.5. Moreover, it contains a unit one-sheeted disk with a radial slit. We apply this result to obtain a universal lower estimate of the Bloch seminorm for finite Blaschke products.

MSC:

30J10 Blaschke products
30F99 Riemann surfaces
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