Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Warszawa
Polska Akad. Nauk, Inst. Matematyczny
2000
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| Schriftenreihe: | Dissertationes mathematicae
388 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 103 S. |
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| 245 | 1 | 0 | |a Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions |c Wlodzimierz Zwonek |
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Datensatz im Suchindex
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| adam_text |
Titel: Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant funct
Autor: Zwonek, WłOdzimierz
Jahr: 2000
CONTENTS
Summary.5
I. Introduction.7
1.1. (Holomorphically) contractible families of functions and pseudometrics.7
1.2. Product property.11
1.3. Various notions of geodesies. Lempert Theorem.12
1.4. Effective formulas for invariant functions.14
1.5. Finite compactness and completeness with respect to invariant distances.17
1.6. Pluricomplex Green function with a logarithmic pole.19
1.7. The Green function with many poles. Analytic disks and the Green function.20
1.8. The Bergman distance. Bergman completeness.22
1.9. Caratheodory balls and norm balls.24
II. Pseudoconvex Reinhardt domains—completeness.25
2.1. Geometry of pseudoconvex Reinhardt domains.25
2.2. Convex cones and pseudoconvex Reinhardt domains.26
2.3. Algebraic mappings.30
2.4. Quasi-elementary Reinhardt domains.31
2.5. Hyperbolicity of pseudoconvex Reinhardt domains.34
2.6. Caratheodory and Kobayashi completeness of pseudoconvex Reinhardt domains. 36
2.7. Bergman completeness of bounded Reinhardt domains.43
2.8. Boundary behavior of the Green function and Bergman completeness.49
III. Effective formulas in Reinhardt domains.54
3.1. Elementary Reinhardt domains with I n.55
3.2. Auxiliary results.56
3.3. Proof of Theorem 3.1.1 in the rational case.63
3.4. Proof of Theorem 3.1.1 in the irrational case.67
3.5. Elementary Reinhardt domains with l = n.70
3.6. The pluricomplex Green function of the unit ball with two poles.72
IV. Symmetry of the pluricomplex Green function.77
4.1. Symmetry of the Green function of complex ellipsoids.77
4.2. Infinitesimal symmetry of the Green function.83
4.3. Nonsymmetry of the Green function of complete Reinhardt domains.88
V. Norm balls and Caratheodory balls in convex ellipsoids.91
List of symbols.97
References.100
2000 Mathematics Subject Classification: 31C10, 32A07, 32A25, 32F45, 32H35, 32U05, 32U35.
Received 22.2.1999; revised version 17.11.1999. |
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| discipline | Mathematik |
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| indexdate | 2025-03-31T20:03:50Z |
| institution | BVB |
| language | English |
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| physical | 103 S. |
| publishDate | 2000 |
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| publisher | Polska Akad. Nauk, Inst. Matematyczny |
| record_format | marc |
| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Zwonek, WłOdzimierz Verfasser aut Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions Wlodzimierz Zwonek Warszawa Polska Akad. Nauk, Inst. Matematyczny 2000 103 S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 388 Domains of holomorphy Geodesics (Mathematics) Green's functions Invariants Dissertationes mathematicae 388 (DE-604)BV000003039 388 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009136683&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zwonek, WłOdzimierz Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions Dissertationes mathematicae Domains of holomorphy Geodesics (Mathematics) Green's functions Invariants |
| title | Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions |
| title_auth | Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions |
| title_exact_search | Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions |
| title_full | Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions Wlodzimierz Zwonek |
| title_fullStr | Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions Wlodzimierz Zwonek |
| title_full_unstemmed | Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions Wlodzimierz Zwonek |
| title_short | Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions |
| title_sort | completeness reinhardt domains and the method of complex geodesics in the theory of invariant functions |
| topic | Domains of holomorphy Geodesics (Mathematics) Green's functions Invariants |
| topic_facet | Domains of holomorphy Geodesics (Mathematics) Green's functions Invariants |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009136683&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003039 |
| work_keys_str_mv | AT zwonekwłodzimierz completenessreinhardtdomainsandthemethodofcomplexgeodesicsinthetheoryofinvariantfunctions |