Bergman local isometries are biholomorphisms

Jihun Yum

doi:10.1142/S0129167X26500059

Bergman local isometries are biholomorphisms

Jihun Yum^*

^*Corresponding author for this work

Department of Mathematics Education

Research output: Contribution to journal › Journal article › peer-review

Abstract

In this paper, we prove that a proper holomorphic local isometry between bounded domains with respect to the Bergman metrics is necessarily a biholomorphism. The proof relies on a new method grounded in Information Geometry theories.

Original language	English
Article number	2650005
Journal	International Journal of Mathematics
Volume	37
Issue number	1
DOIs	https://doi.org/10.1142/S0129167X26500059
State	Published - 2026.01.1

Keywords

Bergman local isometry
Bergman metric
biholomorphism
sufficient statistics

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10.1142/S0129167X26500059

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title = "Bergman local isometries are biholomorphisms",

abstract = "In this paper, we prove that a proper holomorphic local isometry between bounded domains with respect to the Bergman metrics is necessarily a biholomorphism. The proof relies on a new method grounded in Information Geometry theories.",

keywords = "Bergman local isometry, Bergman metric, biholomorphism, sufficient statistics",

author = "Jihun Yum",

note = "Publisher Copyright: {\textcopyright} 2026 World Scientific Publishing Company.",

year = "2026",

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doi = "10.1142/S0129167X26500059",

language = "English",

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N2 - In this paper, we prove that a proper holomorphic local isometry between bounded domains with respect to the Bergman metrics is necessarily a biholomorphism. The proof relies on a new method grounded in Information Geometry theories.

AB - In this paper, we prove that a proper holomorphic local isometry between bounded domains with respect to the Bergman metrics is necessarily a biholomorphism. The proof relies on a new method grounded in Information Geometry theories.

KW - Bergman local isometry

KW - Bergman metric

KW - biholomorphism

KW - sufficient statistics

UR - https://www.scopus.com/pages/publications/105022464352

U2 - 10.1142/S0129167X26500059

DO - 10.1142/S0129167X26500059

M3 - Journal article

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VL - 37

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 1

M1 - 2650005

ER -

Bergman local isometries are biholomorphisms

Abstract

Keywords

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