Graham type theorem on classical bounded symmetric domains

Graham Theorem on the unit ball B n in C n states that every invariant harmonic function u ∈ C n ( B ¯ n ) must be pluriharmonic in B n (Graham in Commun Partial Differ Equ 8(5):433–476, 1983 ). This rigidity phenomenon of Graham has been studied by many authors [see, for examples, Graham and Lee (D...

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Published inCalculus of variations and partial differential equations Vol. 58; no. 2; pp. 1 - 25
Main Authors Chen, Ren-Yu, Li, Song-Ying
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2019
Springer Nature B.V
Subjects
Analysis
Calculus of Variations and Optimal Control; Optimization
Control
Domains
Harmonic functions
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theorems
Theoretical
Laplace–Beltrami operator
35J70
Primary 32A50
Invariant harmonic
35R01
Secondary 32T15
Bounded symmetric domains
Pluriharmonic
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Summary:Graham Theorem on the unit ball B n in C n states that every invariant harmonic function u ∈ C n ( B ¯ n ) must be pluriharmonic in B n (Graham in Commun Partial Differ Equ 8(5):433–476, 1983 ). This rigidity phenomenon of Graham has been studied by many authors [see, for examples, Graham and Lee (Duke Math J 57:697–720, 1988 ), Li and Simon (Am J Math 124:1045–1057, 2002 ), Li and Wei (Sci China Math 53:779–790, 2010 ), etc]. In this paper, we prove that Graham theorem holds on classical bounded symmetric domains, which include Type I and Type II domains, Type III domain III(n) and Type IV domain IV( n ) with even n ≥ 4 .
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-019-1517-0