论文标题
重量下统一结构域的共形转换取决于到边界的距离
Conformal transformation of uniform domains under weights that depend on distance to the boundary
论文作者
论文摘要
球形化过程将欧几里得空间转换为紧凑的球体。在本说明中，我们提出了此过程的变体，以使用仅取决于仅取决于到达度量空间边界的距离的保形变形，以局部紧凑的路径连接，不完整的无界度量空间。该变形是局部Bi-Lipschitz到其边界附近的原始域，但将空间转换为有限的域。我们将证明，如果原始度量空间相对于其完成是统一的域，则转换的空间也是一个统一的域。
The sphericalization procedure converts a Euclidean space into a compact sphere. In this note we propose a variant of this procedure for locally compact, rectifiably path-connected, non-complete, unbounded metric spaces by using conformal deformations that depend only on the distance to the boundary of the metric space. This deformation is locally bi-Lipschitz to the original domain near its boundary, but transforms the space into a bounded domain. We will show that if the original metric space is a uniform domain with respect to its completion, then the transformed space is also a uniform domain.
