A Remark on the Kernel of the CR Paneitz operator

2015/02/06 by Jeffrey S. Case, Case, Jeffrey S., Sagun Chanillo +3 · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1502.01992

openalex publication_date 2015/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For CR structures in dimension three, the CR pluriharmonic functions are characterized by the vanishing of a third order operator. This third order operator, after composition with the divergence operator, gives the fourth order analogue of the Paneitz operator. In this short note, we give criteria under which the kernel of the CR Paneitz operator contains a supplementary space to the CR pluriharmonic functions.

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