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Removability and non-injectivity of conformal welding

2017/03/02 by Younsi, Malik
#30C85 #Complex Variables (math.CV) #FOS: Mathematics #primary 30C35 #secondary 37E10

paper · doi:10.48550/arxiv.1703.00974

Abstract

We construct a (non-removable) Jordan curve Γ and a non-Möbius homeomorphism of the Riemann sphere which is conformal on the complement of Γ and maps the curve Γ onto itself. The curve is flexible in the sense of Bishop and may be taken to have zero area. The existence of such curves and conformal homeomorphisms is closely related to the non-injectivity of conformal welding.

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