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Lectures on counterexamples in several complex variables

Author: John Erik Fornæss; Berit Stensønes
Publisher: Providence, R.I. : AMS Chelsea Pub./American Mathematical Society, [2007]
Series: AMS Chelsea Publishing, v.363.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Counterexamples are remarkably effective for understanding the meaning, and the limitations, of mathematical results. Fornæss and Stensønes look at some of the major ideas of several complex variables by considering counterexamples to what might seem like reasonable variations or generalizations. The first part of the book reviews some of the basics of the theory, in a self-contained introduction to several complex  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Fornæss, John Erik.
Lectures on counterexamples in several complex variables /
(DLC) 2007026106
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: John Erik Fornæss; Berit Stensønes
ISBN: 9781470431204 1470431203
OCLC Number: 973203435
Notes: Originally published: Princeton, N.J. : Princeton University Press ; [Tokyo] : University of Tokyo Press, 1987.
Description: 1 online resource (247 pages : illustrations).
Contents: Some notations and definitions Holomorphic functions Holomorphic convexity and domains of holomorphy Stein manifolds Subharmonic/Plurisubharmonic functions Pseudoconvex domains Invariant metrics Biholomorphic maps Counterexamples to smoothing of plurisubharmonic functions Complex Monge Ampère equation $H^\infty $-convexity CR-manifolds Pseudoconvex domains without pseudoconvex exhaustion Stein neighborhood basis Riemann domains over $\mathbb {C}^n$ The Kohn-Nirenberg example Peak points Bloom's example D'Angelo's example Integral manifolds Peak sets for A(D) Peak sets. Steps 1-4 Sup-norm estimates for the $\bar {\partial }$-equation Sibony's $\bar {\partial }$-example Hypoellipticity for $\bar {\partial }$ Inner functions Large maximum modulus sets Zero sets Nontangential boundary limits of functions in $H^\infty (\mathbb {B}^n)$ Wermer's example The union problem Riemann domains Runge exhaustion Peak sets in weakly pseudoconvex boundaries The Kobayashi metric.
Series Title: AMS Chelsea Publishing, v.363.
Responsibility: John Erik Fornæss, Berit Stensønes.

Abstract:

Counterexamples are remarkably effective for understanding the meaning, and the limitations, of mathematical results. Fornæss and Stensønes look at some of the major ideas of several complex variables by considering counterexamples to what might seem like reasonable variations or generalizations. The first part of the book reviews some of the basics of the theory, in a self-contained introduction to several complex variables. The counterexamples cover a variety of important topics: the Levi problem, plurisubharmonic functions, Monge-Ampère equations, CR geometry, function theory, and the \bar\

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