2025/01/10 by Rodriguez, Alex
#30C85 (Primary) #30E25 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.06347
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.