The Kobayashi pseudometric for the Fock-Bargmann-Hartogs domain and its application

2018/12/18 by Enchao Bi, Bi, Enchao, Guicong Su +3
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1812.07338

to appear in Journal of Geometric Analysis

arxiv created 2018/12/18 · openalex publication_date 2018/12/18 · arxiv updated 2018/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Fock-Bargmann-Hartogs domain D_n,m in ℂ^n+m is defined by the inequality ‖w‖²<e^-‖z‖2, where (z,w)∈ ℂⁿ× ℂ^m, which is an unbounded non-hyperbolic domain in ℂ^n+m. This paper mainly consists of three parts. Firstly, we give the explicit expression of geodesics of D_n,1 in the sense of Kobayashi pseudometric; Secondly, using the formula of geodesics, we calculate explicitly the Kobayashi pseudometric on D_1,1; Lastly, we establish the Schwarz lemma at the boundary for holomorphic mappings between the nonequidimensional Fock-Bargmann-Hartogs domains by using the formula for the Kobayashi pseudometric on D_1,1.

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