Bergman local isometries are biholomorphisms

2024/04/29 by Jihun Yum, Yum, Jihun
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2404.18792

openalex publication_date 2024/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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