A symplectic functional analytic proof of the conformal welding theorem

Schippers, Eric; Staubach, Wolfgang

doi:10.1090/S0002-9939-2014-12225-8

A symplectic functional analytic proof of the conformal welding theorem
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by Eric Schippers and Wolfgang Staubach PDF

Proc. Amer. Math. Soc. 143 (2015), 265-278 Request permission

Abstract:

We give a new functional-analytic/symplectic geometric proof of the conformal welding theorem. This is accomplished by representing composition by a quasisymmetric map $\phi$ as an operator on a suitable Hilbert space and algebraically solving the conformal welding equation for the unknown maps $f$ and $g$ satisfying $g \circ \phi = f$. The univalence and quasiconformal extendibility of $f$ and $g$ is demonstrated through the use of the Grunsky matrix.

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