论文标题
准文献几何形状和可移动套件用于保形映射
Quasiconformal geometry and removable sets for conformal mappings
论文作者
论文摘要
我们研究了通过保形重量或更通常是可测量的鳍结构定义的度量空间，该结构在域$ω\ subset \ subset \ mathbb {r}^2 $上消失在紧凑型集合$ e \ subsetω$上并满足的假设。我们的主要问题是确定这种空间何时在形式上等同于平面域。我们从可去除共形映射的平面集的概念方面给出了特征。我们还研究了何时可以将准文献映射的问题计算为用Bi-Lipschitz映射预先构成的1 Quasiconformal映射。
We study metric spaces defined via a conformal weight, or more generally a measurable Finsler structure, on a domain $Ω\subset \mathbb{R}^2$ that vanishes on a compact set $E \subset Ω$ and satisfies mild assumptions. Our main question is to determine when such a space is quasiconformally equivalent to a planar domain. We give a characterization in terms of the notion of planar sets that are removable for conformal mappings. We also study the question of when a quasiconformal mapping can be factored as a 1-quasiconformal mapping precomposed with a bi-Lipschitz map.
