Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 203 / 1 / a

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- Solution a

Solution

A compact H-hull is a bounded, relatively closed set

A \subset H

such that

H ∖ A

is simply connected. Its mapping-out function of a compact H-hull is the unique conformal bijection

g_{A} : H ∖ A ⟶ H

with hydrodynamic normalization

g_{A} (z) = z + \frac{hcap ( A )}{z} + O (∣ z ∣^{- 2}) (z \to \infty) .

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