Work

Domains with Bergman metrics of constant curvature and Bergman‐negligible subsets

Year: 2026

Type: article

Abstract: Let be a bounded domain in . Suppose the holomorphic sectional curvature of its Bergman metric equals a negative constant . We show that is biholomorphic to a domain equal to the unit ball in less a relatively closed set of measure zero, and that all ‐holomorphic functions on extend to ‐holomorphic functions on the ball. Consequently, must equal the holomorphic sectional curvature of the unit ball. This generalizes a classical theorem of Lu. Some applications of the theorem, especially in extending classical work of Wong and Rosay, are also presented.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70678

Authors: Peter Ebenfelt, John N. Treuer, Ming Xiao

Institutions: University of California San Diego, San Jose State University

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Invariants in Several Complex Variables and Complex Geometry, CAREER: Geometric Function Theory in Several Complex Variables, G7760017010, Invariant analysis in several complex variables, CR and complex geometry., Research and Education in Several Complex Variables