VMO-Teichmüller space on the real line
| Autor: | Yuliang Shen |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Teichmüller space Quasiconformal mapping Pure mathematics Universal Teichmüller space quasiconformal mapping VMOA quasisymmetric homeomorphism Articles Banach manifold Beltrami coefficient Carleson measure Homeomorphism (graph theory) BMOA Upper half-plane strongly symmetric homeomorphism Real line vanishing Carleson measure |
| Zdroj: | Annales Fennici Mathematici |
| ISSN: | 2737-114X 2737-0690 |
| DOI: | 10.54330/afm.112456 |
| Popis: | An increasing homeomorphism \(h\) on the real line \(\mathbb{R}\) is said to be strongly symmetric if it can be extended to a quasiconformal homeomorphism of the upper half plane \(\mathbb{U}\) onto itself whose Beltrami coefficient \(\mu\) induces a vanishing Carleson measure \(|\mu(z)|^2/y\,dx\,dy\) on \(\mathbb{U}\). We will deal with the class of strongly symmetric homeomorphisms on the real line and its Teichmüller space, which we call the VMO-Teichmüller space. In particular, we will show that if \(h\) is strongly symmetric on the real line, then it is strongly quasisymmetric such that \(\log h'\) is a VMO function. This improves some classical results of Carleson (1967) and Anderson-Becker-Lesley (1988) on the problem about the local absolute continuity of a quasisymmetric homeomorphism in terms of the Beltrami coefficient of a quasiconformal extension. We will also discuss various models of the VMO-Teichmüller space and endow it with a complex Banach manifold structure via the standard Bers embedding. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|