Invariant distances and metrics in complex analysis /
by Marek Jarnicki, Peter Pflug.
Berlin ; New York : Walter de Gruyter, 1993.
xi, 408 p. : ill. ; 25 cm.
3110132516 (acid-free paper)
More Details
added author
Berlin ; New York : Walter de Gruyter, 1993.
3110132516 (acid-free paper)
catalogue key
Includes bibliographical references (p. [387]-399) and index.
A Look Inside
Table of Contents
Hyperbolic geometry of the unit discp. 1
The Caratheodory pseudodistance and the Caratheodory-Reiffen pseudometricp. 15
Definitions. General Schwarz-Pick Lemmap. 16
Balanced domainsp. 18
Caratheodory hyperbolicityp. 27
The Caratheodory topologyp. 29
Properties of c(*) and [gamma]. Length of curve. Inner Caratheodory pseudodistancep. 33
Two applicationsp. 48
A class of n-circled domainsp. 53
The Kobayashi pseudodistance and the Kobayashi-Royden pseudometricp. 71
The Lempert function and the Kobayashi pseudodistancep. 71
Tautnessp. 77
General properties of kp. 82
An extension theoremp. 87
The Kobayashi-Royden pseudometricp. 90
The Kobayashi-Buseman pseudometricp. 99
Product-formulap. 106
Contractible systemsp. 111
Abstract point of viewp. 111
Extremal problems for plurisubharmonic functionsp. 115
Inner pseudodistances. Integrated forms. Derivatives. Buseman pseudometrics. C[superscript 1]-pseudodistancesp. 139
Example - elementary n-circled domainsp. 149
Contractible functions and metrics for the annulusp. 154
The Bergman metricp. 169
The Bergman kernelp. 169
The Bergman pseudometricp. 185
Comparison and localizationp. 190
The Skwarczynski pseudometricp. 195
Hyperbolicity and completenessp. 202
Global hyperbolicityp. 202
Local hyperbolicityp. 207
Completeness - general discussionp. 213
Caratheodory completenessp. 216
Kobayashi completenessp. 223
Bergman completenessp. 230
Complex geodesics. Lempert's theoremp. 237
Complex geodesicsp. 237
Lempert's theoremp. 243
Uniqueness of complex geodesicsp. 255
Geodesics in convex complex ellipsoidsp. 264
Biholomorphisms of complex ellipsoidsp. 278
Schwarz Lemma - the case of equalityp. 281
Criteria for biholomorphicityp. 285
Product-propertyp. 296
Comparison on strongly pseudoconvex domainsp. 310
Strongly pseudoconvex domainsp. 310
The boundary behavior of the Caratheodory and the Kobayashi distancesp. 316
Localizationp. 326
Boundary behavior of the Caratheodory-Reiffen and the Kobayashi-Royden metricsp. 331
A comparison of distancesp. 342
Characterization of the unit ball by its automorphism groupp. 344
Misc. A The automorphism group of bounded domainsp. 355
Misc. B Holomorphic curvaturep. 356
Misc. C Complex geodesicsp. 359
Misc. D Criteria for biholomorphicityp. 361
Misc. E Boundary behavior of contractible metrics on weakly pseudoconvex domainsp. 363
App. HF Holomorphic functionsp. 367
App. PSH Subharmonic and plurisubharmonic functionsp. 370
App. PSC Domains of holomorphy and pseudoconvex domainsp. 375
App. AUT Automorphismsp. 379
Automorphisms of the unit discp. 379
Automorphisms of the unit polydiscp. 379
Automorphisms of the unit Euclidean ballp. 380
App. GR Green function and Dirichlet problemp. 380
App. MA Monge-Ampere operatorp. 383
App. H Hardy spacesp. 384
Referencesp. 387
List of symbolsp. 400
Indexp. 405
Table of Contents provided by Blackwell. All Rights Reserved.

This information is provided by a service that aggregates data from review sources and other sources that are often consulted by libraries, and readers. The University does not edit this information and merely includes it as a convenience for users. It does not warrant that reviews are accurate. As with any review users should approach reviews critically and where deemed necessary should consult multiple review sources. Any concerns or questions about particular reviews should be directed to the reviewer and/or publisher.

  link to old catalogue

Report a problem