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Biholomorphic invariants related to the Bergman functions

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Skwarczyński M.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS PRELIMINARY REMARKS........................................................................................ 5 Introduction..................................................................................................... 5 Basic definitions, examples and facts............................................................... 8 I. 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...................................... 15 II. REPRESENTATIVE COORDINATES................................................................... 16 The Bergman metric tensor......................................................................... 16 A property of representative coordinates........................................................... 19 III. AN INVARIANT DISTANCE................................................................................... 20 Biholomorphic mappings and canonical isometry................................. 20 Critical points of the invariant distance.............................................................. 22 Completeness with respect to the invariant distance..................................... 22 IV. EXTENSION THEOREM....................................................................................... 27 Semiconformal mappings........................................................................... 27 Extension theorem................................................................................................ 31 Local characterization of a biholomorphic mapping...................................... 33 V. DOMAIN DEPENDENCE...................................................................................... 36 Ramadanov theorem.................................................................................... 36 An analogue of Ramadanov theorem for decreasing sequences................ 37 A counterexample in the plane............................................................................ 39 VI. 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........................................ 54 REFERENCES.............................................................................................................. 58

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A general description of the Bergman projection

42%

Skwarczyński M.

Annales Polonici Mathematici

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1985

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tom 46

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nr 1

311-315

3

The ideal boundary of a domain in $C^n$

42%

Skwarczyński M.

Annales Polonici Mathematici

|

1981

|

tom 39

|

nr 1

213-226

4

L²-Angles between one-dimensional tubes

31%

Skwarczyński M.

Studia Mathematica

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1988

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tom 90

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nr 3

213-233

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Studia Mathematica

4 Skwarczyński M.

1 1988

1 1985

1 1981

1 1980

Biholomorphic invariants related to the Bergman functions

A general description of the Bergman projection

The ideal boundary of a domain in $C^n$

L²-Angles between one-dimensional tubes