Holdings: Invariant distances and metrics in complex analysis

Invariant distances and metrics in complex analysis:

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Bibliographic Details
Main Authors:	Jarnicki, Marek 1952- (Author), Pflug, Peter (Author)
Format:	Book
Language:	English
Published:	Berlin u.a. de Gruyter 1993
Series:	De Gruyter expositions in mathematics 9
Subjects:	Invariante - Metrischer Raum - Pseudometrik Komplexe Funktion Pseudoabstand Pseudometrik Metrischer Raum Invariante Funktionentheorie
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 408 S. Ill.
ISBN:	3110132516

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MARC


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Record in the Search Index

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adam_text	Contents Preface vii I Hyperbolic geometry of the unit disc 1 Exercises 14 II The Caratheodory pseudodistance and the Caratheodory Reiffen pseudometric 15 2.1 Definitions. General Schwarz Pick Lemma 16 2.2 Balanced domains 18 2.3 Caratheodory hyperbolicity 27 2.4 The Caratheodory topology 29 2.5 Properties of c* * 1 and y. Length of curve. Inner Caratheodory pseudodistance 33 2.6 Two applications 48 2.7 A class of n circled domains 53 Notes 65 Exercises 66 III The Kobayashi pseudodistance and the Kobayashi Royden pseudometric 71 3.1 The Lempert function and the Kobayashi pseudodistance . . 71 3.2 Tautness 77 3.3 General properties of k 82 3.4 An extension theorem 87 3.5 The Kobayashi Royden pseudometric 90 3.6 The Kobayashi Buseman pseudometric 99 3.7 Product formula 106 Notes 108 Exercises 109 IV Contractible systems Ill 4.1 Abstract point of view Ill 4.2 Extremal problems for plurisubharmonic functions 115 4.3 Inner pseudodistances. Integrated forms. Derivatives. Buseman pseudometrics. C pseudodistances 139 x Contents 4.4 Example elementary n circled domains 149 Notes 152 Exercises 153 V Contractible functions and metrics for the annulus 154 Notes 165 Exercises 166 VI The Bergman metric 169 6.1 The Bergman kernel 169 6.2 The Bergman pseudometric 185 6.3 Comparison and localization 190 6.4 The Skwarczyriski pseudometric 195 Notes 198 Exercises 200 VII Hyperbolicity and completeness 202 7.1 Global hyperbolicity 202 7.2 Local hyperbolicity 207 7.3 Completeness general discussion 213 7.4 Caratheodory completeness 216 7.5 Kobayashi completeness 223 7.6 Bergman completeness 230 Notes 234 Exercises 235 VIII Complex geodesies. Lempert s theorem 237 8.1 Complex geodesies 237 8.2 Lempert s theorem 243 8.3 Uniqueness of complex geodesies 255 8.4 Geodesies in convex complex ellipsoids 264 8.5 Biholomorphisms of complex ellipsoids 278 8.6 Schwarz Lemma the case of equality 281 8.7 Criteria for biholomorphicity 285 Notes 288 Exercises 290 IX Product property 296 Exercises 309 X Comparison on strongly pseudoconvex domains 310 10.1 Strongly pseudoconvex domains 310 Contents xi 10.2 The boundary behavior of the Caratheodory and the Kobayashi distances 316 10.3 Localization 326 10.4 Boundary behavior of the Caratheodory Reiffen and the Kobayashi Royden metrics 331 10.5 A comparison of distances 342 10.6 Characterization of the unit ball by its automorphism group . 344 Notes 352 Exercises 353 Miscellanea 355 A The automorphism group of bounded domains 355 B Holomorphic curvature 356 C Complex geodesies 359 D Criteria for biholomorphicity 361 E Boundary behavior of contractible metrics on weakly pseudoconvex domains 363 Appendix 367 HF Holomorphic functions 367 PSH Subharmonic and plurisubharmonic functions 370 PSC Domains of holomorphy and pseudoconvex domains .... 375 AUT Automorphisms 379 Automorphisms of the unit disc 379 Automorphisms of the unit polydisc 379 Automorphisms of the unit Euclidean ball 380 GR Green function and Dirichlet problem 380 MA Monge Ampere operator 383 H Hardy spaces 384 References 387 List of symbols 400 Index 405
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author	Jarnicki, Marek 1952- Pflug, Peter
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spelling	Jarnicki, Marek 1952- Verfasser (DE-588)101811095X aut Invariant distances and metrics in complex analysis by Marek Jarnicki ; Peter Pflug Berlin u.a. de Gruyter 1993 XI, 408 S. Ill. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 9 Invariante - Metrischer Raum - Pseudometrik Komplexe Funktion (DE-588)4217733-9 gnd rswk-swf Pseudoabstand (DE-588)4335987-5 gnd rswk-swf Pseudometrik (DE-588)4176150-9 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Invariante (DE-588)4128781-2 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Komplexe Funktion (DE-588)4217733-9 s Pseudoabstand (DE-588)4335987-5 s Invariante (DE-588)4128781-2 s Metrischer Raum (DE-588)4169745-5 s DE-604 Funktionentheorie (DE-588)4018935-1 s Pseudometrik (DE-588)4176150-9 s 1\p DE-604 Pflug, Peter Verfasser aut De Gruyter expositions in mathematics 9 (DE-604)BV004069300 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004847173&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Jarnicki, Marek 1952- Pflug, Peter Invariant distances and metrics in complex analysis De Gruyter expositions in mathematics Invariante - Metrischer Raum - Pseudometrik Komplexe Funktion (DE-588)4217733-9 gnd Pseudoabstand (DE-588)4335987-5 gnd Pseudometrik (DE-588)4176150-9 gnd Metrischer Raum (DE-588)4169745-5 gnd Invariante (DE-588)4128781-2 gnd Funktionentheorie (DE-588)4018935-1 gnd
subject_GND	(DE-588)4217733-9 (DE-588)4335987-5 (DE-588)4176150-9 (DE-588)4169745-5 (DE-588)4128781-2 (DE-588)4018935-1
title	Invariant distances and metrics in complex analysis
title_auth	Invariant distances and metrics in complex analysis
title_exact_search	Invariant distances and metrics in complex analysis
title_full	Invariant distances and metrics in complex analysis by Marek Jarnicki ; Peter Pflug
title_fullStr	Invariant distances and metrics in complex analysis by Marek Jarnicki ; Peter Pflug
title_full_unstemmed	Invariant distances and metrics in complex analysis by Marek Jarnicki ; Peter Pflug
title_short	Invariant distances and metrics in complex analysis
title_sort	invariant distances and metrics in complex analysis
topic	Invariante - Metrischer Raum - Pseudometrik Komplexe Funktion (DE-588)4217733-9 gnd Pseudoabstand (DE-588)4335987-5 gnd Pseudometrik (DE-588)4176150-9 gnd Metrischer Raum (DE-588)4169745-5 gnd Invariante (DE-588)4128781-2 gnd Funktionentheorie (DE-588)4018935-1 gnd
topic_facet	Invariante - Metrischer Raum - Pseudometrik Komplexe Funktion Pseudoabstand Pseudometrik Metrischer Raum Invariante Funktionentheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004847173&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV004069300
work_keys_str_mv	AT jarnickimarek invariantdistancesandmetricsincomplexanalysis AT pflugpeter invariantdistancesandmetricsincomplexanalysis

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