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arXiv · 2003.10013

Functional Determinant on Pseudo-Einstein 3-manifolds

Ali Maalaoui
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Abstract

Given a three dimensional pseudo-Einstein CR manifold $(M,T^{1,0}M,\theta)$, we establish an expression for the difference of determinants of the Paneitz type operators $A_{\theta}$, related to the problem of prescribing the $Q'$-curvature, under the conformal change $\theta\mapsto e^{w}\theta$ with $w\in \P$ 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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Ali Maalaoui. 2020-03-22. Functional Determinant on Pseudo-Einstein 3-manifolds. https://doi.org/10.2140/pjm.2020.309.421

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