vix.ing · top · new · best · stats · spec

Conformal weldings in the Loewner equation and Weil--Petersson quasislit-disks

2024/10/18 by Tao, Fei, Wei, Huaying, Yang, Yaosong
#30C62 #30C75 #30H25 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.14346

Abstract

A simple arc Γ= γ(0, T], growing into the unit disk \mathbb D from its boundary, generates a driving term ξ and a conformal welding ϕ through the Loewner differential equation. When Γ is the slit of a Weil--Petersson quasislit-disk \mathbb D∖Γ, the Loewner transform and its inverse Γ↔ ξ have been well understood due to Y. Wang's work. We investigate the maps Γ↔ ϕ in this case, giving a description of Γ in terms of ϕ.

Related