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As in the field of "Invariant Distances and Metrics in Complex Analysis" there was and is a continuous progress this is now the second extended edition of the corresponding monograph. This comprehensive book is about the study of invariant pseudodistances (non-negative functions on pairs of points) and pseudometrics (non-negative functions on the tangent bundle) in several complex variables. It is an overview over a highly active research area at the borderline between complex analysis, functional analysis and differential geometry. New chapters are covering the Wu, Bergman and several other metrics.
The book considers only domains in Cn and assumes a basic knowledge of several complex variables. It is a valuable reference work for the expert but is also accessible to readers who are knowledgeable about several complex variables. Each chapter starts with a brief summary of its contents and continues with a short introduction. It ends with an "Exercises" and a "List of problems" section that gathers all the problems from the chapter. The authors have been highly successful in giving a rigorous but readable account of the main lines of development in this area.
"This is a comprehensive and beautifully written book about the study of invariant pseudodistances (nonnegative functions on pairs of points) and pseudometrics (nonnegative functions on the tangent bundle) in several complex variables. […] It will be a valuable reference work for the expert but is also accessible to readers who are knowledgeable about several complex variables. There are exercises at the end of each chapter, and unsolved problems are indicated throughout the text. The authors have been highly successful in giving a rigorous but readable account of the main lines of development in this area." Mathematical Reviews (review of the first edition)
"I warmly recommend this monograph, which according to the authors "present[s] a systematic study of invariant pseudodistances and their infinitesimal counterparts". It is a valuable work for the expert, but it is also accessible to readers who are knowledgeable about several complex variables." Mathematical Reviews
"This new extended version is a comprehensive and beautifully-written book and covers more than twice the material in the old one. […] The authors have been highly successful in achieving the main goal of the book, which was, according to their own words, "to present a systematic study of invariant pseudodistances and their infinitesimal counterparts". Moreover, they were able to do that combining great precision of reasoning with highest level of readability." Zentralblatt für Mathematik
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