On Carleson measures induced by Beltrami coefficients being compatible with Fuchsian groups

On Carleson Measures of Beltrami Coefficients Being Compatible with Infinitely Generated Fuchsian Groups Related to Denjoy Domian

Let $Ω$ be a Carleson-Denjoy domain and $G$ be its covering group. Let $μ$ be a Beltrami coefficient on the unit disk which is compatible with the group $G$. In this paper we show that if $\frac{|μ|^{2}}{1-|z|^{2}}dxdy$ satisfies the Carleson condition on the infinite boundary of the Dirichlet fundamental domain of $G$, then $\frac{|μ|^{2}}{1-|z|^{2}}dxdy$ is a Carleson measure on the unit disk. We also show that the above property does not hold for Denjoy domain.

Strongly quasisymmetirc homeomorphisms being compatible with Fuchsian groups

In this paper we first introduced a domain called generalized Dirichlet fundamental domain $\mathcal{F}^{*}$ for a Fuchsian group $G$ whose generators contain parabolic elements. This allows us to show that a quasisymmetric homeomorphism $h$ being compatible with a convergence Fuchsian group $G$ of first kind is a strongly quasisymmetric homeomorphism if and only if it has a quasiconformal extension $f$ to the upper half plane $\mathbb{H}$ onto itself such that the induced measure $λ_μ=|μ|^{2}/Im(z)dxdy$ by the Beltrami coefficient $μ$ of $f$ is a Carleson measure on the generalized Dirichlet …

通过纯线性系统求解Beltrami方程的数值解

Numerical solution of the Beltrami equation via a purely linear system

本文提出了一种在平面圆盘上通过纯线性系统求解Beltrami方程的有效算法，利用三角剖分和分段线性映射，通过稀疏超定方程组的标准最小二乘法求解，无需奇异积分或迭代过程。

Beurling-Carleson集、内函数与一个半线性方程

Beurling-Carleson sets, inner functions and a semi-linear equation

本文综述了Beurling-Carleson集的定义与性质，利用corona型分解揭示了奇异测度的多项性质与该集可数并集的等价关系，并证明了其与半线性方程近最大解的双射对应。