Uniform Estimates for the Hyperbolic Metric and Euclidean Distance to the Boundary

摘要

Throughout this article, D is a proper subdomain of the complex plane C possess- ing at least two finite boundary points, usually termed a hyperbolic domain. Each such D carnes constant negative curvature metrics, and we let An denote the scale factor or density for the maximal constant curvature -l metric. We call An the Poincare' hyperbolic metric for D.