Graham Theorem on Bounded Symmetric Domains

2017/08/11 by Renyu Chen, Ren-Yu Chen, Chen, Ren-Yu +2
Mathematics · #35J70 #35R01 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Primary 32A50 #Secondary 32T15 #math.CV #msc:32A50 #msc:32T15 #msc:35J70 #msc:35R01

paper · pdf · doi:10.48550/arxiv.1708.03434

23pages

arxiv created 2017/08/11 · openalex publication_date 2017/08/11 · arxiv updated 2017/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Graham Theorem on the unit ball B_n in ℂⁿ states that every invariant harmonic function u∈ Cⁿ(B_n) must be pluriharmonic in B_n. This rigidity phenomenon of Graham have been studied by many authors. In this paper, we prove that Graham theorem holds on classical bounded symmetric domains. Which include Type I domains, Type II domains, Type III domains III(n) with even n and some special Type IV domains.

Related

• Invariant plurisubharmonic functions on non-compact Hermitian symmetric spaces
• A symmetry problem
• Positive Pluriharmonic Functions on Symmetric Siegel Domains
• Stable geometric properties of pluriharmonic and biholomorphic mappings, and Landau-Bloch's theorem
• Hua system and pluriharmonicity for symmetric irreducible Siegel domains of type II