Chaudri, Muhammad Hayat.2009-04-172009-04-1719661966Source: Masters Abstracts International, Volume: 45-06, page: 3169.http://hdl.handle.net/10393/10480http://dx.doi.org/10.20381/ruor-16846In this thesis we investigate the distortion caused by an analytic map f : B → W, between the Bergman metric dsB of a bounded domain B in the complex z-plane and the Euclidean metric of the complex w-plane W. We deduce sharp inequalities in the cases of the unit disc, the punctured hyperbolic plane and the annuli, and the minimizing maps are determined.31 p.Mathematics.Thesis