Lectures on Counterexamples in Several Complex Variables (AMS Chelsea Publishing No. 363)

Lectures on Counterexamples in Several Complex Variables (AMS Chelsea Publishing No. 363)

By: John Erik Fornaess (author), Berit Stensones (author)Hardback

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Description

Counterexamples are remarkably effective for understanding the meaning, and the limitations, of mathematical results. Fornaess and Stensones 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-Ampere equations, CR geometry, function theory, and the $\bar\partial$ equation. The book would be an excellent supplement to a graduate course on several complex variables.

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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 Ampere 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 Bibliography.

Product Details

  • publication date: 15/10/2007
  • ISBN13: 9780821844229
  • Format: Hardback
  • Number Of Pages: 247
  • ID: 9780821844229
  • weight: 624
  • ISBN10: 0821844229

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