Invariant Pseudodistances and Pseudometrics in Complex Analysis in Several Variables

Sammanfattning: At present time invariant pseudodistances and pseudometrics pose an important tool in complex analysis in several variables. This thesis is mainly devoted to giving a thorough definition of these objects and in particular to Schwarz-Pick systems such as the Carathéodory and Kobayashi pseudodistances. Most basic properties, such as continuity and boundary behaviour, of the Carathéodory and Kobayashi pseudo-distances and pseudometrics are investigated. As an application of the theory, the thesis is concluded with a proof of the biholomorphic inequivalence between the unit ball and unit polydisc in Cn.