论文标题
高拓扑的度量表面的规范参数化
Canonical parametrizations of metric surfaces of higher topology
论文作者
论文摘要
我们为Bonk和Kleiner对统一定理的以下概括提供了另一种证据。任何线性局部连接和AHLFOR的2个规则闭合度量表面在准对称上等同于同一拓扑的模型表面。此外，我们表明，对于上述具有非空边界的表面也是如此，并且可以以规范的方式选择相应的地图。我们的证明是基于涉及公制盘的准对称参数化的局部论证，如Lytchak和Wenger论文所示。
We give an alternate proof to the following generalization of the uniformization theorem by Bonk and Kleiner. Any linearly locally connected and Ahlfors 2-regular closed metric surface is quasisymmetrically equivalent to a model surface of the same topology. Moreover, we show that this is also true for surfaces as above with non-empty boundary and that the corresponding map can be chosen in a canonical way. Our proof is based on a local argument involving the existence of quasisymmetric parametrizations for metric discs as shown in in a paper of Lytchak and Wenger.
