A Paneitz-Type Operator for CR Pluriharmonic Functions
by Jeffrey S. Case   Paul Yang  

Vol. 8 No. 3 (2013) P.285~P.322

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.

KEYWORDS
pluriharmonic functions, pseudo-Einstein, Paneitz operator, Q-curvature, P-prime operator, Q-prime operator

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 32V05, 53C24

MILESTONES

Received: 2013-07-20
Revised : 2013-08-02
Accepted: 2013-08-03

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