Lectures on Several Complex Variables by Paul M. GauthierLectures on Several Complex Variables by Paul M. Gauthier

Lectures on Several Complex Variables

byPaul M. Gauthier

Paperback | November 27, 2014

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???This monograph provides a concise, accessible snapshot of key topics in several complex variables, including the Cauchy Integral Formula, sequences of holomorphic functions, plurisubharmonic functions, the Dirichlet problem, and meromorphic functions.  Based on a course given at Université de Montréal, this brief introduction covers areas of contemporary importance that are not mentioned in most treatments of the subject, such as modular forms, which are essential for Wiles' theorem and the unification of quantum theory and general relativity.   Also covered is the Riemann manifold of a function, which generalizes the Riemann surface of a function of a single complex variable and is a topic that is well-known in one complex variable, but rarely treated in several variables.  Many details, which are intentionally left out, as well as many theorems are stated as problems, providing students with carefully structured instructive exercises.


Prerequisites for use of this book are functions of one complex variable, functions of several real variables, and topology, all at the undergraduate level.  Lectures on Several Complex Variables will be of interest to advanced undergraduate and beginning undergraduate students, as well as mathematical researchers and professors.

Title:Lectures on Several Complex VariablesFormat:PaperbackDimensions:110 pagesPublished:November 27, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319115103

ISBN - 13:9783319115108


Table of Contents

Preface.- Introduction.- Basics.- Cauchy Integral Formula.- Sequences of Holomorphic Functions.- Series.- Zero Sets of Holomorphic Functions.- Holomorphic Mappings.- Plurisubharmonic Functions.- The Dirichlet Problem.- Uniform Approximation.- Complex Manifolds.- Examples of Manifolds.- Holomorphic Continuation.- The Tangent Space.- Meromorphic Functions and Subvarieties.

Editorial Reviews

"This book grew out of a course given at the Universitéde Montréal in 2004. . The book can be read comfortably by a reader with noprior exposure to several complex variables. . This is also a book with which abeginning graduate student, or even a research mathematician seeking anintroduction to several complex variables, can spend a leisurely summer . andpick up more than just the rudiments of several complex variables." (GautamBharali, Mathematical Reviews, October, 2015)