Lectures on Counterexamples in Several Complex Variables (Google eBook)

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American Mathematical Soc. - Mathematics - 247 pages
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Contents

Some Nations and Definitions
2
Holomorphic Functions
6
Holomorphic Convexity and Domains of Holomorphy
11
Stein Manifolds
17
Subharmonic Functions cont
21
Subharmonic Functions cont
26
Subharmonic Functions cont
31
Plurisubharmonic Functions
34
The KohnNirenberg Example
119
Peak Points
123
Blooms Example
126
DAngelos Example
129
Integral Manifolds
133
Peak Sets for AD
138
Peak Sets Step 1
141
Peak Sets Step 2
145

Plurisubharmonic Functions cont
37
Pseudoconvex Domains
42
Pseudoconvex Domains cont
46
Pseudoconvex Domains cont
50
Invariant Metrics
55
Biholomorphic
60
Counterexamples to Smoothing of Plurisubharmonic Functions
66
Counterexamples to Smoothing of Plurisubharmonic Functions cont
69
Counterexamples to Smoothing of Plurisubharmonic Functions cont
73
Counterexamples to Smoothing of Plurisubharmonic Functions cont
79
Complex Monge Ampére Equation
83
HConvexity
87
CRManifolds
91
CRManifolds cont
95
CRManifolds cont
100
Pseudoconvex Domains without Pseudoconvex Exhaustion
102
Stein Neighborhood Basis
105
Stein Neighborhood Basis cont
109
Stein Neighborhood Basis cont
113
Riemann Domains over ⁿ
115
Peak Sets Step 3
148
Peak Sets Step 4
159
SupNorm Estimates for the əEquation
165
Sibonys əExample
168
Hypoellipticity for ə
174
Inner Functions
178
Inner Functions cont
184
Large Maximum Modulus Sets
189
Zero Sets
194
Nontangential Boundary Limits of Functions in H𝔹ⁿ
202
Wermers Example
212
The Union Problem
214
Riemann Domains
218
Runge Exhaustion
222
Runge Exhaustion cont
227
Peak Sets in Weakly Pseudoconvex Boundaries
229
Peak Sets in Weakly Pseudoconvex Boundaries cont
234
The Kobayashi Metric
236
Bibligraphy
242
Copyright

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