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 $w \in 𝒫$ the space of pluriharmonic functions. This generalizes the expression of the functional determinant in four-dimensional Riemannian manifolds established in (Proc. Amer. Math. Soc. 113:3 (1991), 669–682). We also provide an existence result of maximizers for the scaling invariant functional determinant as in (Ann. of Math. $(2)$ 142:1 (1995), 171–212).

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Keywords

pseudo-Einstein CR manifolds, functional determinant, the $P'$-operator

Mathematical Subject Classification

Primary: 58J35, 58J50

Secondary: 32V05, 32V20

Milestones

Received: 16 August 2020

Revised: 6 October 2020

Accepted: 9 October 2020

Published: 14 January 2021

Authors

Ali Maalaoui
Department of Mathematics and Computer Science Clark University Worcester, MA United States	Department of Mathematics and Natural Sciences American University of Ras Al Khaimah Ras Al Khaimah United Arab Emirates

Vol. 309, No. 2, 2020

Ali Maalaoui

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors