Estimates for the hyperbolic metric of the punctured plane and applications (Q5951478)

The authors obtain new estimates for the hyperbolic metric of the twice punctured complex plane, based on symmetrization and polarization transformations. A recursive algorithm for computing its density is presented. Some applications to meromorphic functions and quasiconformal mappings are given. In particular, the authors answer a question of G. Martin on quasiconformal mappings of a proper subdomain of the punctured plane that can be extended to the complement of the subdomain as the identity map. Some open problems are discussed as well.