A Paneitz-type operator for CR pluriharmonic functions

2013/09/10 by Jeffrey S. Case, Case, Jeffrey S., Paul Yang +1 · 1 citation
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1309.2528

openalex publication_date 2013/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a fourth order CR invariant operator on pluriharmonic functions on a three-dimensional CR manifold, generalizing to the abstract setting the operator discovered by Branson, Fontana and Morpurgo. For a distinguished class of contact forms, all of which have vanishing Hirachi-Q curvature, these operators determine a new scalar invariant with properties analogous to the usual Q-curvature. We discuss how these are similar to the (conformal) Paneitz operator and Q-curvature of a four-manifold, and describe its relation to some problems for three-dimensional CR manifolds.

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