2021/11/28 by Wei, Huaying, Matsuzaki, Katsuhiko · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2111.14011
Similarly to the Bers simultaneous uniformization, the product of the p-Weil-Petersson Teichmüller spaces for p ≥ 1 provides the coordinates for the space of p-Weil-Petersson embeddings γ of the real line \mathbb R into the complex plane \mathbb C. We prove the biholomorphic correspondence from this space to the p-Besov space of u=log γ' on \mathbb R for p>1. From this fundamental result, several consequences follow immediately which clarify the analytic structures concerning parameter spaces of p-Weil-Petersson curves. In particular, it follows that the correspondence of the Riemann mapping parameters to the arc-length parameters keeping the images of curves is a homeomorphism with bi-real-analytic dependence of change of parameters. This is a counterpart to a classical theorem of Coifman and Meyer for chord-arc curves.