论文标题
与紫红色群体兼容强烈的准中甲。
Strongly quasisymmetirc homeomorphisms being compatible with Fuchsian groups
论文作者
论文摘要
在本文中，我们首先引入了一个称为概括的dirichlet基本域$ \ mathcal {f}^{*} $的域，用于fuchsian $ g $，其发电机包含抛物线元素。这使我们能够证明，与融合的fuchsian $ g $兼容的准对称同型同构$ h $第一类是一种很强的准对象同构时，只有当它具有quasiconformal $ f $ to to to to to plane for to to plane plane $ f $ f $ f $ f $ f $ f $ f。 $λ_μ= |μ|^{2}/im（z）dxdy $ by beltrami系数$ f $ $ f $是carleson的carleson量度，对广义的dirichlet基本域$ \ nathcal $ \ mathcal {f}^{*}^{**} $ 我们还表明，上述属性也适用于Carleson-Denjoy域。
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 fundamental domain $\mathcal{F}^{*}.$ We also show that the above property also holds for Carleson-Denjoy domains.
