Tailiang Liu

collaborators

5 papers

math.CV2026

A Compactness Characterization of Strongly Symmetric Homeomorphisms

Liu Tailiang, Shen Yuliang

A self-homeomorphism $h$ of the unit circle $T$ is strongly symmetric if it is absolutely continuous and $lo g h^{'} \in VMO (T)$ . Let $P_{h}^{-}$ be the anti-analyt…

math.CV2026

Conformal welding of chord-arc curves

Liu Tailiang

We study the relation between the geometric properties of a chord-arc curve and its conformal welding. Let $h$ be the conformal welding of a closed quasicircle $Γ$ . By Jones's theo…

math.CV2026

Real-analytic realization of universal Teichmüller space via complex-structures on $H^{1/2}$

Liu Tailiang, Shen Yuliang

Let $H$ be the Hilbert transform, let $h$ be a quasisymmetric homeomorphism of the unit circle $S^{1}$ , and set $V_{h} u = u \circ h$ and $J_{h} = V_{h} H V_{h}^{- 1}$ , defined on the Sobolev space $…

math.CV2026

Conformally Invariant Besov Spaces on Chord-Arc Domains

Liu Tailiang, Shen Yuliang, Yang Yaosong

Let $Γ$ be a rectifiable Jordan curve. We introduce the associated Besov $p$ -spaces on $Γ$ and in its complementary domains, and characterize chord-arc curves by the natural trace…

math.CV2024

The boundary correspondence under quasiconformal mappings and VMO-Teichmuller space

Liu Tailiang, Shen Yuliang

In this paper, we introduce a class of vanishing Carleson measures with conformal invariance and corresponding strongly vanishing symmetric homeomorphisms on the real line and prov…

A Compactness Characterization of Strongly Symmetric Homeomorphisms

Conformal welding of chord-arc curves

Real-analytic realization of universal Teichmüller space via complex-structures on H1/2

Conformally Invariant Besov Spaces on Chord-Arc Domains

The boundary correspondence under quasiconformal mappings and VMO-Teichmuller space

Real-analytic realization of universal Teichmüller space via complex-structures on $H^{1/2}$