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Lectures on Counterexamples in Several Complex Variables
About this Title
John Erik Fornæss, University of Michigan, Ann Arbor, Ann Arbor, MI and Berit Stensønes, University of Michigan, Ann Arbor, Ann Arbor, MI
Publication: AMS Chelsea Publishing
Publication Year:
1987; Volume 363
ISBNs: 978-0-8218-4422-9 (print); 978-1-4704-3120-4 (online)
DOI: https://doi.org/10.1090/chel/363
ReadershipTable of Contents
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Front/Back Matter
Lectures on counterexamples in several complex variables
- 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