Real methods in complex and CR geometry: lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30 - July 6, 2002
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Series: | Lecture notes in mathematics
1848 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 218 S. graph. Darst. |
| ISBN: | 3540223584 |
Staff View
MARC
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| 245 | 1 | 0 | |a Real methods in complex and CR geometry |b lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30 - July 6, 2002 |c Marco Abate ... Ed. D. Zaitsev ... |
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| 650 | 7 | |a Problème aux valeurs limites |2 rasuqam | |
| 650 | 7 | |a Variedades complexas (congressos) |2 larpcal | |
| 650 | 7 | |a Variété complexe |2 rasuqam | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Angular Derivatives in Several Complex Variables
Marco Abate 1
1 Introduction 1
2 One Complex Variable 4
3 Julia s Lemma 12
4 Lindelof Principles 21
5 The Julia Wolff Caratheodory Theorem 32
References 45
Real Methods in Complex Dynamics
John Erik ForneEss 49
1 Lecture 1: Introduction to Complex Dynamics and Its Methods 49
1.1 Introduction 49
1.2 General Remarks on Dynamics 53
1.3 An Introduction to Complex Dynamics and Its Methods 56
2 Lecture 2: Basic Complex Dynamics in Higher Dimension 62
2.1 Local Dynamics 62
2.2 Global Dynamics 71
2.3 Fatou Components 74
3 Lecture 3: Saddle Points for Henon Maps 77
3.1 Elementary Properties of Henon Maps 78
3.2 Ergodicity and Measure Hyperbolicity 79
3.3 Density of Saddle Points 83
4 Lecture 4: Saddle Hyperbolicity for Henon Maps 87
4.1 J and J* 87
4.2 Proof of Theorem 4.10 91
4.3 Proof of Theorem 4.9 96
References 105
VIII Contents
Local Equivalence Problems for Real Submanifolds in
Complex Spaces
Xiaojun Huang 109
1 Global and Local Equivalence Problems 109
2 Formal Theory for Levi Non degenerate Real Hypersurfaces 113
2.1 General Theory for Formal Hypersurfaces 113
2.2 7 4 Space and Hypersurfaces in the ft* Normal Form 119
2.3 Application to the Rigidity and Non embeddability Problems ... 124
2.4 Chern Moser Normal Space Mch 128
3 Bishop Surfaces with Vanishing Bishop Invariants 129
3.1 Formal Theory for Bishop Surfaces
with Vanishing Bishop Invariant 131
4 Moser Webster s Theory on Bishop Surfaces
with Non exceptional Bishop Invariants 140
4.1 Complexification M. of M and a Pair
of Involutions Associated with M 141
4.2 Linear Theory of a Pair of Involutions Intertwined
by a Conjugate Holomorphic Involution 142
4.3 General Theory on the Involutions
and the Moser Webster Normal Form 144
5 Geometric Method to the Study of Local Equivalence Problems 147
5.1 Cartan s Theory on the Equivalent Problem 147
5.2 Segre Family of Real Analytic Hypersurfaces 153
5.3 Cartan Chern Moser Theory for Germs
of Strongly Pseudoconvex Hypersurfaces 159
References 161
Introduction to a General Theory of Boundary Values
Jean Pierre Rosay 165
1 Introduction Basic Definitions 167
1.1 What Should a General Notion of Boundary Value Be? 167
1.2 Definition of Strong Boundary Value (Global Case) 167
1.3 Remarks on Smooth (Not Real Analytic) Boundaries I68
1.4 Analytic Functionals 168
1.5 Analytic Functional as Boundary Values I68
1.6 Some Basic Properties of Analytic Functionals 169
Carriers Martineau s Theorem I69
Local Analytic Functionals I70
1.7 Hyperfunctions 170
The Notion of Functional (Analytic Functional or Distribution,
etc.) Carried by a Set, Defined Modulo Similar
Functionals Carried by the Boundary of that Set I70
Hyperfunctions 171
1.8 Limits 172
Contents IX
2 Theory of Boundary Values on the Unit Disc 172
2.1 Functions u(t,6) That Have Strong Boundary Values
(Along t = 0) 173
2.2 Boundary Values of Holomorphic Functions on the Unit Disc ... 173
2.3 Independence on the Defining Function 174
2.4 The Role of Subharmonicity (Illustrated Here by Discussing
the Independence on the Space of Test Functions) 175
3 The Hahn Banach Theorem in the Theory of Analytic Functional ... 177
3.1 A Hahn Banach Theorem 178
3.2 Some Comments 178
3.3 The Notion of Good Compact Set 180
3.4 The Case of Non Stein Manifolds 180
4 Spectral Theory 181
5 Non linear Paley Wiener Theory and Local Theory
of Boundary Values 182
5.1 The Paley Wiener Theory 182
5.2 Application 186
5.3 Application to a Local Theory of Boundary Values 186
References 189
Extremal Discs and the Geometry of CR. Manifolds
Alexander Tumanov 191
1 Extremal Discs for Convex Domains 192
2 Real Manifolds in Complex Space 192
3 Extremal Discs and Stationary Discs 195
4 Coordinate Representation of Stationary Discs 197
5 Stationary Discs for Quadrics 199
6 Existence of Stationary Discs 201
7 Geometry of the Lifts 203
8 Defective Manifolds 205
9 Regularity of CR Mappings 207
10 Preservation of Lifts 209
References 212
|
| any_adam_object | 1 |
| author | Abate, Marco |
| author_facet | Abate, Marco |
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| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 322f |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-raw | 510 515/.946 |
| dewey-search | 510 515/.946 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T19:59:06Z |
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| spelling | Abate, Marco Verfasser aut Real methods in complex and CR geometry lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30 - July 6, 2002 Marco Abate ... Ed. D. Zaitsev ... Berlin [u.a.] Springer 2004 IX, 218 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1848 CR-sous-variété rasuqam CR-sous-variétés - Congrès Complexe manifolds gtt Dynamique complexe rasuqam Problème aux valeurs limites rasuqam Variedades complexas (congressos) larpcal Variété complexe rasuqam Variétés complexes - Congrès CR submanifolds Congresses Complex manifolds Congresses Komplexe Geometrie (DE-588)4164898-5 gnd rswk-swf Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2002 Martina Franca gnd-content Komplexe Geometrie (DE-588)4164898-5 s Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 s DE-604 Zaitsev, Dmitri Sonstige oth Lecture notes in mathematics 1848 (DE-604)BV000676446 1848 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012849814&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abate, Marco Real methods in complex and CR geometry lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30 - July 6, 2002 Lecture notes in mathematics CR-sous-variété rasuqam CR-sous-variétés - Congrès Complexe manifolds gtt Dynamique complexe rasuqam Problème aux valeurs limites rasuqam Variedades complexas (congressos) larpcal Variété complexe rasuqam Variétés complexes - Congrès CR submanifolds Congresses Complex manifolds Congresses Komplexe Geometrie (DE-588)4164898-5 gnd Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 gnd |
| subject_GND | (DE-588)4164898-5 (DE-588)4147400-4 (DE-588)1071861417 |
| title | Real methods in complex and CR geometry lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30 - July 6, 2002 |
| title_auth | Real methods in complex and CR geometry lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30 - July 6, 2002 |
| title_exact_search | Real methods in complex and CR geometry lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30 - July 6, 2002 |
| title_full | Real methods in complex and CR geometry lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30 - July 6, 2002 Marco Abate ... Ed. D. Zaitsev ... |
| title_fullStr | Real methods in complex and CR geometry lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30 - July 6, 2002 Marco Abate ... Ed. D. Zaitsev ... |
| title_full_unstemmed | Real methods in complex and CR geometry lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30 - July 6, 2002 Marco Abate ... Ed. D. Zaitsev ... |
| title_short | Real methods in complex and CR geometry |
| title_sort | real methods in complex and cr geometry lectures given at the c i m e summer school held in martina franca italy june 30 july 6 2002 |
| title_sub | lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30 - July 6, 2002 |
| topic | CR-sous-variété rasuqam CR-sous-variétés - Congrès Complexe manifolds gtt Dynamique complexe rasuqam Problème aux valeurs limites rasuqam Variedades complexas (congressos) larpcal Variété complexe rasuqam Variétés complexes - Congrès CR submanifolds Congresses Complex manifolds Congresses Komplexe Geometrie (DE-588)4164898-5 gnd Cauchy-Riemannsche Mannigfaltigkeit (DE-588)4147400-4 gnd |
| topic_facet | CR-sous-variété CR-sous-variétés - Congrès Complexe manifolds Dynamique complexe Problème aux valeurs limites Variedades complexas (congressos) Variété complexe Variétés complexes - Congrès CR submanifolds Congresses Complex manifolds Congresses Komplexe Geometrie Cauchy-Riemannsche Mannigfaltigkeit Konferenzschrift 2002 Martina Franca |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012849814&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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