Biholomorphic invariants related to the Bergman functions

Maciej Skwarczyński

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1980

Abstract

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CONTENTSPRELIMINARY REMARKS........................................................................................ 5 Introduction..................................................................................................... 5 Basic definitions, examples and facts............................................................... 8I. LU QI-KENQ DOMAINS........................................................................................... 13 Some properties of Lu Qi-keng domains.................................................. 13 An example of bounded non-Lu Qi-keng domain............................................ 14 Doubly connected Lu Qi-keng domains in the plane...................................... 15II. REPRESENTATIVE COORDINATES................................................................... 16 The Bergman metric tensor......................................................................... 16 A property of representative coordinates........................................................... 19III. AN INVARIANT DISTANCE................................................................................... 20 Biholomorphic mappings and canonical isometry................................. 20 Critical points of the invariant distance.............................................................. 22 Completeness with respect to the invariant distance..................................... 22IV. EXTENSION THEOREM....................................................................................... 27 Semiconformal mappings........................................................................... 27 Extension theorem................................................................................................ 31 Local characterization of a biholomorphic mapping...................................... 33V. DOMAIN DEPENDENCE...................................................................................... 36 Ramadanov theorem.................................................................................... 36 An analogue of Ramadanov theorem for decreasing sequences................ 37 A counterexample in the plane............................................................................ 39VI. THE IDEAL BOUNDARY....................................................................................... 40 Definition of the ideal boundary................................................................... 40 Characteristic properties....................................................................................... 49 The case of bounded circular domains.............................................................. 53 Plane domains and strictly pseudoconvex domains........................................ 54REFERENCES.............................................................................................................. 58

How to cite

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Maciej Skwarczyński. Biholomorphic invariants related to the Bergman functions. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1980. <http://eudml.org/doc/268383>.

@book{MaciejSkwarczyński1980,
abstract = {CONTENTSPRELIMINARY REMARKS........................................................................................ 5 Introduction..................................................................................................... 5 Basic definitions, examples and facts............................................................... 8I. LU QI-KENQ DOMAINS........................................................................................... 13 Some properties of Lu Qi-keng domains.................................................. 13 An example of bounded non-Lu Qi-keng domain............................................ 14 Doubly connected Lu Qi-keng domains in the plane...................................... 15II. REPRESENTATIVE COORDINATES................................................................... 16 The Bergman metric tensor......................................................................... 16 A property of representative coordinates........................................................... 19III. AN INVARIANT DISTANCE................................................................................... 20 Biholomorphic mappings and canonical isometry................................. 20 Critical points of the invariant distance.............................................................. 22 Completeness with respect to the invariant distance..................................... 22IV. EXTENSION THEOREM....................................................................................... 27 Semiconformal mappings........................................................................... 27 Extension theorem................................................................................................ 31 Local characterization of a biholomorphic mapping...................................... 33V. DOMAIN DEPENDENCE...................................................................................... 36 Ramadanov theorem.................................................................................... 36 An analogue of Ramadanov theorem for decreasing sequences................ 37 A counterexample in the plane............................................................................ 39VI. THE IDEAL BOUNDARY....................................................................................... 40 Definition of the ideal boundary................................................................... 40 Characteristic properties....................................................................................... 49 The case of bounded circular domains.............................................................. 53 Plane domains and strictly pseudoconvex domains........................................ 54REFERENCES.............................................................................................................. 58},
author = {Maciej Skwarczyński},
keywords = {biholomorphic invariants; Bergman function; biholomorphic transformation; semiconformal mapping; Lu Qi-keng domain; invariant distance; Kobayashi conjecture; strictly pseudoconvex domain},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Biholomorphic invariants related to the Bergman functions},
url = {http://eudml.org/doc/268383},
year = {1980},
}

TY - BOOK
AU - Maciej Skwarczyński
TI - Biholomorphic invariants related to the Bergman functions
PY - 1980
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSPRELIMINARY REMARKS........................................................................................ 5 Introduction..................................................................................................... 5 Basic definitions, examples and facts............................................................... 8I. LU QI-KENQ DOMAINS........................................................................................... 13 Some properties of Lu Qi-keng domains.................................................. 13 An example of bounded non-Lu Qi-keng domain............................................ 14 Doubly connected Lu Qi-keng domains in the plane...................................... 15II. REPRESENTATIVE COORDINATES................................................................... 16 The Bergman metric tensor......................................................................... 16 A property of representative coordinates........................................................... 19III. AN INVARIANT DISTANCE................................................................................... 20 Biholomorphic mappings and canonical isometry................................. 20 Critical points of the invariant distance.............................................................. 22 Completeness with respect to the invariant distance..................................... 22IV. EXTENSION THEOREM....................................................................................... 27 Semiconformal mappings........................................................................... 27 Extension theorem................................................................................................ 31 Local characterization of a biholomorphic mapping...................................... 33V. DOMAIN DEPENDENCE...................................................................................... 36 Ramadanov theorem.................................................................................... 36 An analogue of Ramadanov theorem for decreasing sequences................ 37 A counterexample in the plane............................................................................ 39VI. THE IDEAL BOUNDARY....................................................................................... 40 Definition of the ideal boundary................................................................... 40 Characteristic properties....................................................................................... 49 The case of bounded circular domains.............................................................. 53 Plane domains and strictly pseudoconvex domains........................................ 54REFERENCES.............................................................................................................. 58
LA - eng
KW - biholomorphic invariants; Bergman function; biholomorphic transformation; semiconformal mapping; Lu Qi-keng domain; invariant distance; Kobayashi conjecture; strictly pseudoconvex domain
UR - http://eudml.org/doc/268383
ER -

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