Vol. 309, No. 2, 2020

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Functional determinant on pseudo-Einstein 3-manifolds

Ali Maalaoui

Vol. 309 (2020), No. 2, 421–436
Abstract

Given a three-dimensional pseudo-Einstein CR manifold (M,T1,0M,𝜃), we establish an expression for the difference of determinants of the Paneitz type operators A𝜃, related to the problem of prescribing the Q-curvature, under the conformal change 𝜃ew𝜃 with w 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).

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