标题： 拟对称Koebe定理在度量曲面上的统一化 显示英文标题

标题： Quasisymmetric Koebe Uniformization of metric surfaces

摘要： 我们研究度量曲面$X$何时可以共形映射到具有均匀相对分离边界成分的圆域$D\subset\mathbb{C}$。Bonk\cite{Bonk}证明了如果$X\subset \hat{\mathbb{C}}$且$X$的边界成分是均匀相对分离的准圆，则$X$与圆域共形。Merenkov 和 Wildrick\cite{Merenkov Wildrick}表明在非平面情况下，Bonk 的条件是不充分的。我们在一些温和假设下证明，度量曲面与具有均匀相对分离边界成分的圆域共形当且仅当它是 2-TLP。 后者是Bonk引入并研究的一种条件的版本，\cite{Bonk}。 这回答了Merenkov和Wildrick在\cite{Merenkov Wildrick}提出的问题，同时也是将Bonk的结果自然推广到非平面度量曲面的情况。 显示英文摘要

摘要： We study when a metric surface $X$ can be mapped quasisymmetrically onto a circle domain $D\subset\mathbb{C}$ with uniformly relatively separated boundary components. Bonk \cite{Bonk} proved that if $X\subset \hat{\mathbb{C}}$ and the boundary components of $X$ are uniformly relatively separated uniform quasicircles then $X$ is quasisymmetric to a circle domain. Merenkov and Wildrick \cite{Merenkov Wildrick} showed that Bonk's condition is not sufficient in the non-planar case. We prove that under some mild assumptions, a metric surface is quasisymmetric to a circle domain with uniformly relatively separated boundary components if and only if it is 2-TLP. The latter is a version of a condition introduced and studied by Bonk \cite{Bonk}. This answers a question of Merenkov and Wildrick in \cite{Merenkov Wildrick} and it is also a natural generalization of Bonk's result to non-planar metric surfaces.