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Defining functions and cores of unbounded domains
Core sets of unbounded domains
Holomorphic extension of CR functions and the CR-core
A CR-core with no analytic structure
Introduction
Unbounded Wermer type sets
Construction of Wermer type sets in codimension 1
The general construction
Some geometric properties
Choice of constants - Part I. Absence of analytic structure
Choice of constants - Part II. Complete pluripolarity
A Liouville theorem for Wermer type sets
Construction of Wermer type sets in codimension k
The general construction
Generalization of results to the case of codimension k
Pseudoconcavity and degeneration of plurisubharmonic functions
Core sets of unbounded domains
Global plurisubharmonic defining functions and the core
Existence of global plurisubharmonic defining functions
Existence results in complex manifolds
Existence results in complex spaces
Examples of unbounded domains with nonempty core
1-pseudoconcavity of the core
Liouville type properties of the core
Pseudoconcavity of higher order cores
Holomorphic extension of CR functions and the CR-core
A CR-core with no analytic structure
Comparison of the core and the CR-core
Open Questions
Bibliography
Dissertation
Defining functions and cores of unbounded domains / von Tobias Harz
Entstehung
Wuppertal
2015
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