arXiv subjects

Huaying Wei

Publications and source records attributed to Huaying Wei.

24 records · Page 2Linked to original sources

arXiv2019

Teichmüller spaces of piecewise symmetric homeomorphisms on the unit circle

We interpolate a new family of Teichmüller spaces $T_{\sharp}^X$ between the universal Teichmüller space $T$ and its little subspace $T_0$, which we call the Teichmüller space of piecewise symmetric homeomorphisms. This is defined by prescribing a subset $X$ of the unit circle. The inclusion relation of $X$ induces a natural inclusion of $T_{\sharp}^X$, and an approximation of $T$ is given by an increasing sequence of $T_{\sharp}^X$. In this paper, we discuss the fundamental properties of $T_{\sharp}^X$ from the viewpoint of the quasiconformal theory of Teichmüller spaces. We also consider the quotient space of $T$ by $T_{\sharp}^X$ as an analog of the asymptotic Teichmüller space.

math.CV↗

arXiv2019

Teichmüller spaces of generalized symmetric homeomorphisms

We introduce the concept of a new kind of symmetric homeomorphisms on the unit circle, which is derived from the generalization of symmetric homeomorphisms on the real line. By the investigation of the barycentric extension for this class of circle homeomorphisms and the biholomorphic automorphisms induced by trivial Beltrami coefficients, we endow a complex Banach manifold structure on the space of those generalized symmetric homeomorphisms.

math.CV↗

arXiv2018

BMO Teichmüller spaces and their quotients with complex and metric structures

The paper presents some recent results on the BMO Teichmüller space, its subspaces and quotient spaces. We first consider the chord-arc curve subspace and prove that every element of the BMO Teichmüller space is represented by its finite composition. Moreover, we show that these BMO Teichmüller spaces have affine foliated structures induced by the VMO Teichmüller space. By which, their quotient spaces have natural complex structures modeled on the quotient Banach space. Then, a complete translation-invariant metric is introduced on the BMO Teichmüller space and is shown to be a continuous Finsler metric in a special case.

math.CV↗

arXiv2018

Ahlfors-regular curves and Carleson measures

We study the relation between the boundary of a simply connected domain being Ahlfors-regular and the invariance of Carleson measures under the push-forward operator induced by a conformal mapping from the unit disk onto the domain. As an application, we characterize the chord-arc curve with small norm and the asymptotically smooth curve in terms of the complex dilatation of some quasiconformal reflection with respect to the curve.

math.CV↗

arXiv2017

Carleson measures and chord-arc curves

Following Semmes and Zinsmeister, we continue the study of Carleson measures and their invariance under pull-back and push-forward operators. We also study the analogous statements for vanishing Carleson measures. As an application, we show that some quotient space of the space of chord-arc curves has a natural complex structure.

math.CV↗

arXiv2017

BMO-Teichmüller spaces revisited

In a paper of Cui and Zinsmeister the equivalence among three definitions of BMO-Teichmüller spaces associated with a Fuchsian group was proven using the Douady-Earle extension operator. In this paper, we show that these equivalences are actually biholomorphisms. It was further shown in the above quoted paper that the Douady-Earle extension operator is continuous at the origin. We improve this result by showing Gâteaux-differentiability at this point.

math.CV↗