Every circle homeomorphism is the composition of two weldings
classification
🧮 math.CV
keywords
compositionlog-singularcapacitycircleconformaleveryhomeomorphismhomeomorphisms
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We show that every orientation-preserving circle homeomorphism is a composition of two conformal welding homeomorphisms, which implies that conformal welding homeomorphisms are not closed under composition. Our approach uses the log-singular maps introduced by Bishop. The main tool that we introduce are log-singular sets, which are zero capacity sets that admit a log-singular map that maps their complement to a zero capacity set.
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Cited by 1 Pith paper
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