Functional Determinant on Pseudo-Einstein 3-manifolds

Given a three dimensional pseudo-Einstein CR manifold $(M,T^{1,0}M,θ)$, we establish an expression for the difference of determinants of the Paneitz type operators $A_θ$, related to the problem of prescribing the $Q'$-curvature, under the conformal change $θ\mapsto e^{w}θ$ with $w\in ¶$ the space of pluriharmonic functions. This generalizes the expression of the functional determinant in four dimensional Riemannian manifolds established in \cite{BO2}. We also provide an existence result of maximizers for the scaling invariant functional determinant as in \cite{CY}.

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