Extension of internally bilipschitz maps in John disks.
Broch, Ole Jacob (2006)
Annales Academiae Scientiarum Fennicae. Mathematica
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Extension of internally bilipschitz maps in John disks.
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The aim of this work is to answer positively a more general question than the following which is due to T. Sheil-Small: Does the harmonic extension in the open unit disc of a mapping f from the unit circle into itself of the form f(eit) = eiϕ(t), 0 ≤ t ≤ 2π, where ϕ is a continuously non-decreasing function that satisfies ϕ(2π)−ϕ(0) = 2Nπ, assume every value finitely many times in the disc?
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