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arXiv · 1309.2528

A Paneitz-type operator for CR pluriharmonic functions

Jeffrey S. Case·Paul Yang
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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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Jeffrey S. Case, Paul Yang. 2013-09-10. A Paneitz-type operator for CR pluriharmonic functions. https://arxiv.org/abs/1309.2528

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