论文标题
高拓扑的度量表面的准表面均匀化
Quasiconformal uniformization of metric surfaces of higher topology
论文作者
论文摘要
我们为度量$ x $有限的Hausdorff 2量化建立了以下统一结果。如果$ x $对具有非空边界的平滑2个manifold $ m $同型，那么我们表明$ x $仅假设$ x $是本地地理位置，并且有可纠正的边界，则仅假设$ x $是列出的几乎参数化$ m \ to x $。特别是，我们通过使用高原问题的解决方案来恢复Ntalampekos和Romney的推论。在对$ x $上提出了其他假设后，我们表明，准文献几乎参数化升级到准对称或几何形式形式形式图中，这意味着类似于Bonk和Kleiner的统一定理的陈述，以及Rajala以及Rajala的较高拓扑表面。
We establish the following uniformization result for metric spaces $X$ of finite Hausdorff 2-measure. If $X$ is homeomorphic to a smooth 2-manifold $M$ with non-empty boundary, then we show that $X$ admits a quasiconformal almost parametrization $M\to X$, by only assuming that $X$ is locally geodesic and has rectifiable boundary. In particular, we recover a corollary of Ntalampekos and Romney by using the solution of the Plateau problem. After putting additional assumptions on $X$, we show that the quasiconformal almost parametrization upgrades to a quasisymmetry or a geometrically quasiconformal map, implying statements analogous to the uniformization theorems of Bonk and Kleiner as well as Rajala for surfaces of higher topology.
